Suppose that the functions s and t are defined for all real numbers x as follows. s (x) = 4x-3 t (x) =x+2 Write the expressions for (s – t)(x) and (s t) (x) and evaluate (s +t)(3). (s – t)(x) = [| (s-t) (x) = ] (s + t)(3) = ]

Q: a) If g(x) = 2x + 10 and h(x) = 3x - 2, 3 Find: - g[h(x)] = and express in its simplest form b) If…

A: Since in the given question in part (b) you asked for g inverse but there is a function f so, we…

Q: Suppose that 2 <f '(x) < 4 for all values of x. What are the minimum and maximum possible values of…

A: Using Mean Value Theorm.

Q: Find (go f)(x) if f(x) = 2x2 – 3x and g(x) = x + 2 O 2x2 + 5x + 2 O 2x2 + 5x + 8 O 2x? – 3x +2 O…

A: Given: fx=2x2-3x and gx=x+2 To find: gofx

Q: The function f(x) = x -x2 - x- is graphed in 11 %3D 4 the xy-plane above. If k is a constant such…

A:

Q: (b) Suppose that f(x) : УBx2 — 3 (Bx +2 if if x 2 Find the value of ß so that f(x) is continuous…

A:

Q: The absolute maximum value of the function f(x) =x3 – 12x +4 on the closed interval [-1,3] is equal…

A: Topic = Application of derivative Absolute maximum value is 15.

Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7 X = - 2 and x = 6 x = 2 and…

A:

Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: If f(x) = 4x2 + 1 satisfies Rolle's Theorem on [a, 2], then a = 2 -1 -2 none

A:

Q: The function f(x) = 2x³ – 36x² + 192x - 3 has two critical numbers. The smaller one is x = and the…

A:

Q: If g(x) = 2x + 10 and h(x) = 3x - 2,                        3 Find: - g[h(x)] = and express in its…

A:

Q: If f(x) = 3x — 7, find the image of 2 and the preimage of 2

A: Given: fx=3x-7 To determine: Image &amp; pre-image of 2.

Q: If f'(x) and g'(x) exist and f'(x) > g(x) for all real a, then the graph of y = f(x) and the graph…

A: In this question we have to find how many time functions will intersect to each other.

Q: The equation of a quartic function with zeros -5, 1, and 3 with an order 2 is: * O f(x) = k(x - 3)(x…

A: We have to find the equation of quartic function with zeros -5, 1 and 3 with an order 2. Since,…

Q: Find k such that f(x) = x4 - kx3 + kx2 + 1 has the factor x + 2.

A:

Q: 4. Prove that if f(x) = aox" + a,x"-1+ ...+ an-1x = 0 has a positive root x = xo, then the equation…

A: Roll's theorem: If f is continuous function on [a, b], differentiable on (a, b) and f(a) = f(b) then…

Q: 2. Consider a ball thrown in the air (f) defined by the formula f(x) = (3 + x)^2 whose domain is the…

A:

Q: Let k(x) f(x)g(x) h(x) If f (x) = 3x, g(x) = x - 2, and h(x) = -x² + x + 1, what is k' (x)? %3D…

A: We know that, from quotient rule of differentiation We have,  fx=3x, gx=x-2 and hx=-x2+x+1 Now,…

Q: Determine the constants a and b so that x = -1 is a zero point to q (x) = x5-3bx3 + ax2-ax + b with…

A:

Q: 4. Consider f(x) = 2x² + 3 on the closed interval I = [0, 4].

A: I have Provided this answer in step-2. i have given an only one answer because as per our policy.

Q: If f(x) = 2x² + 4x - 3, then f(x+h)-f(x) h 012x+ +2h)²+(4x+4h)−3−(2x²+4x-3) h 2(x+h)² +4x−3−2x² -…

A:

Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

A:

Q: Let f(x) = 3x -2 and let g(x) = 5x + 5. Find f(x) - g(x). %3D %3D Type the coefficients in the…

A:

Q: Let f(x) = x³ +x + 4 and g(x) = 3x + 2 in Zs[x). Then, upon dividing f(x) by g(x), we get None of…

A: Every integer polynomial we can write as an polynomial in Z5(x). Using this idea again and again we…

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

A:

Q: The critical numbers of the function f(x) = x³ – 6x2 are x = 0 and x = -4. Select one: True O False

A: Given; fx=x3-6x2   As we know that; To calculate the critical numbers of the function, f'x=0.   And…

Q: 4) Show that and 4x 2 - 4x f(x) = 4x-2 4-4x are eventually fixed points for the function : 0<x<…

A: Given

Q: If f^(x)=c for some natural number n and constant c, then f is a polynomial function. True or false?

A:

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

A: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

Q: 6. (a) Express f (x), where x3 + 1 f(x) = %3D (x – 1)2 (x² + 1) Hence, or, otherwise, find HE AND…

A: f(x)=x3+1(x-1)2(x2+1)

Q: The function f(x) =is 1-z2 Is 9+z2

A:

Q: Prove that the real part of is constant for -n < 0 < n z+2-i

A: Let  z = a+ib

Q: f(x) = x³ – 3x²

A: Given: f(x) =x3 -3x2 -9x +27

Q: If g(y) is differentiable for 2<_y<_3 (<_ means less than or equal) and g(2) =g(3)=-1, then there is…

A: There is one theorem i.e. Rolle's theorem states that if a function f is continuous on the closed…

Q: 4 If f'(x) = x³ x'-2x +x+2, then f has inflection points at 3. n X=0 X= -0.5 X-1 x-0.6 X-2

A: Point of inflection  Those points where cancavity changes called inflection points

Q: Find (f 1)(a) for f(7)=0, f'(1)=-1, and a=0. -л -1 1/л -1/n

A: topic - derivative of inverse function

Q: 4) Show that and are eventually fixed points for the function : 8 4x Osx< 2- 4x sx< f(x) = - 1 4x –…

A:

Q: Find a number c that satisfies the conclusion for f(x) = x + x-1 on the interval [0, 2]

A: Answer is 2/√3

Q: Find f for the function z = - 3x6 0 02-30x4 ex ax = ex 7x8 1 8 6x 02-02-63 x = 6xy + 4y2.

A: This question can be solved using the concept of partial derivatives.

Q: Find the critical number of f(x) = 3x^2 - 18x + 4

A:

Q: Find an nth-degree polynomial function with real coefficients satisfying the given condition n = 3;…

A: Our Aim is to find an nth-degree polynomial function with real coefficients satisfying the given…

Q: Suppose z is a function of r and y, and x² + y² + z² = xe² + ye² + ze³. Solve əz əz for and əx ду

A: Topic = Derivative

Q: I have no idea how to approach this question.  Any insight would be greatly appreciated.

A:

Q: there is at most one polynomial of degree less than or equal to n_____ option,(a) which interpolated…

A: Using interpolation theory, We need to check which option is correct.

Q: 9. For the polynomial function f(x)= x³ - bx² + cx-24 where b,cel, all of the following are…

A: The given function is a cubic polynomial: f(x)=x3-bx2+cx-24     , here b,c∈I If p is a zero of that…

Q: Let h(x)=−2x^2+x+4/x^2+4x−1, what is h′(−5)?

A:

Q: 5. Find the domain of the function: y = In () x-4

A: y=lnx-1x-4

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the Chain Rule, Product Rule and Quotient Rule to check the claim.