Problem 1AYU: Find f( 3 ) if f( x )=4 x 2 +5x . (pp. 60-62) Problem 2AYU: Find f(3x) if f(x)=42 x 2 . (pp. 60-62) Problem 3AYU: Find the domain of the function f(x)= x 2 1 x 2 25 . (pp. 64-66) Problem 4AYU: Given two functions f and g , the _____, denoted fg , is defined by (fg)(x)= _____. Problem 5AYU: True or False If f(x)= x 2 and g(x)= x+9 , then (fg)(4)=5 . Problem 6AYU: If f(x)= x+2 and g(x)= 3 x , which of the following does (fg)(x) equal? a. 3 x+2 b. 3 x +2 c. 3 x +2... Problem 7AYU: If H=fg and H(x)= 254 x 2 , which of the following cannot be the component functions f and g ? a.... Problem 8AYU: True or False The domain of the composite function (fg)(x) is the same as the domain of g(x) . Problem 9AYU: In Problems 9 and 10, evaluate each expression using the values given in the table. a. ( fg )( 1 )... Problem 10AYU: In Problems 9 and 10, evaluate each expression using the values given in the table. a. ( fg )( 1 )... Problem 11AYU: In Problems 11 and 12, evaluate each expression using the graphs of y=f(x) and y=g(x) shown in the... Problem 12AYU: In Problems 11 and 12, evaluate each expression using the graphs of y=f(x) and y=g(x) shown in the... Problem 13AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 14AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 15AYU: In problems for the given functions and find:
Problem 16AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 17AYU: In problems for the given functions and find:
Problem 18AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 19AYU: In problems 1322, for the given functions f and g, find: (fg)(4) (gf)(2) (ff)(1) (gg)(0) f(x)=|x|;... Problem 20AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 21AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 22AYU: In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )(... Problem 23AYU: In problems for the given functions and find:
State the domain of each composite function,
... Problem 24AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 25AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 26AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 27AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 28AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 29AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 30AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 31AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 32AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 33AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 34AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 35AYU: In problems 2338, for the given functions f and g, find: fg gf ff gg State the domain of each... Problem 36AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 37AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 38AYU: In Problems 23-38, for the given functions f and g , find: a. fg b. gf c. ff d. gg State the domain... Problem 39AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=2x ; g(x)= 1 2 x Problem 40AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=4x ; g(x)= 1 4 x Problem 41AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )= x 3 ; g(x)= x 3 Problem 42AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=x+5 ; g( x )=x5 Problem 43AYU: In problems 3946, show that (fg)(x)=(gf)(x)=x. f(x)=9x6; g(x)=19(x+6) Problem 44AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=43x ; g( x )=( 4x ) Problem 45AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=ax+b ; g(x)= 1 a (xb) a0 Problem 46AYU: In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f(x)= 1 x ; g(x)= 1 x Problem 47AYU: In Problems 47-52, find functions f and g so that fg=H . H(x)= (2x+3) 4 Problem 48AYU: In Problems 47-52, find functions f and g so that fg=H . H(x)= (1+ x 2 ) 3 Problem 49AYU: In Problems 47-52, find functions f and g so that fg=H . H(x)= x 2 +1 Problem 50AYU: In Problems 47-52, find functions f and g so that fg=H . H(x)= 1 x 2 Problem 51AYU: In Problems 47-52, find functions f and g so that fg=H . H(x)=| 2x+1 | Problem 52AYU: In Problems 47-52, find functions f and g so that fg=H . H(x)=| 2 x 2 +3 | Problem 53AYU: If f(x)=2 x 3 3 x 2 +4x1 and g(x)=2 , find (fg)( x ) and (gf)( x ) . Problem 54AYU: If f(x)= x+1 x1 , find (ff)( x ) . Problem 55AYU: If f(x)=2 x 2 +5 and g(x)=3x+a , find a so that the graph of fg crosses the y-axis at 23. Problem 56AYU: If f(x)=3 x 2 7 and g( x )=2x+a , find a so that the graph of fg crosses the y-axis at 68. Problem 57AYU: In Problems 57 and 58, use the functions f and g to find: a. fg b. gf c. the domain of fg and of gf... Problem 58AYU: In Problems 57 and 58, use the functions f and g to find: a. fg b. gf c. the domain of fg and of gf... Problem 59AYU: Surface Area of a Balloon The surface area S (in square meters) of a hot-air balloon is given by... Problem 60AYU: Volume of a Balloon. The volume V (in cubic meters) of the hot-air balloon described in Problem 59... Problem 61AYU: Automobile Production The number N of cars produced at a certain factory in one day after t hours of... Problem 62AYU: Environmental Concerns The spread of oil leaking from a tanker is in the shape of a circle. If the... Problem 63AYU: Production Cost The price p , in dollars, of a certain product and the quantity x sold obey the... Problem 64AYU: Cost of a Commodity The price p , in dollars, of a certain commodity and the quantity X sold obey... Problem 65AYU: Volume of a Cylinder The volume V of a right circular cylinder of height h and radius r is V= r 2 h... Problem 66AYU: Volume of a Cone The volume V of a right circular cone is V= 1 3 r 2 h . If the height is twice the... Problem 67AYU: Foreign Exchange Traders often buy foreign currency in the hope of making money when the currencys... Problem 68AYU: Temperature Conversion The function C(F)= 5 9 ( F32 ) converts a temperature in degrees Fahrenheit,... Problem 69AYU: Discounts The manufacturer of a computer is offering two discounts on last year’s model computer.... Problem 70AYU: Taxes Suppose that you work for 15 per hour. Write a function that represents gross salary G as a... Problem 71AYU: Suppose f(x)=x3+x216x16 and g(x)=x24. Find the zeros of (fg)(x). Problem 72AYU:
Suppose and
Find the zeros of
Problem 73AYU: Let f( x )=ax+b and g( x )=bx+a , where a and b are integers. if f( 1 )=8 and f(g( 20 ))g(f( 20... Problem 74AYU: If f and g are odd functions, show that the composite function fg is also odd. Problem 75AYU: If f is an odd function and g is an even function, show that the composite functions fg and gf are... Problem 76AYU:
Challenge Problem If and find a, b and c.
Problem 77AYU:
Challenge Problem Given three functions and Define Find if and
Problem 78AYU: Challenge Problem If f(x)=1x+4, g(x)=xx2, and h(x)=x+3. find the domain of (fgh)(x). Problem 79AYU: Problems 74-77 are based on material learned earlier in the course. The purpose of these problems is... Problem 80AYU: Problems are based on material learned earlier in the course. The purpose of these problems is to... Problem 81AYU: Problems 74-77 are based on material learned earlier in the course. The purpose of these problems is... Problem 82AYU: Problems are based on material learned earlier in the course. The purpose of these problems is to... Problem 83AYU: Problems 7988 are based on material learned earlier in the course. The purpose of these problems is... Problem 84AYU: Problems are based on material learned earlier in the course. The purpose of these problems is to... Problem 85AYU: Problems are based on material learned earlier in the course. The purpose of these problems is to... Problem 86AYU: Problems 7988 are based on material learned earlier in the course. The purpose of these problems is... Problem 87AYU: Problems are based on material learned earlier in the course. The purpose of these problems is to... Problem 88AYU: Problems are based on material learned earlier in the course. The purpose of these problems is to... format_list_bulleted