1. The functions fi(x) = 4x, f2(x) = x² + 6x, and fз(x) = 4x² + 12x do not form a linearly independent set of functions. Verify this by writing one of the given functions as a linear combination of the other two functions. (4 pts.)

Q: If  f(x) = 3x + 1  and g(x)=4/x.find f(g(x)) and g(f(x)).

A: Given f(x)=3x+1 and g(x)=4x we have to find f(g(x)), g(f(x))

Q: Determine whether the given set of functions is linearly independent on the interval (-o, ∞). f1(x)…

A: The solution is given as

Q: find h(1) = 1 + h(-1), h(2), h(+), h(x – 1), h

A:

Q: Consider the functions, h(x) = 3x – 7 and k(x) = . b. Find h(k(x)) X+7 | a. Find h(k(- 2)) c. Find…

A:

Q: Find f(x) and g(x) such that h(x) = (fog)(x). 4 h(x) = (6x+3)* Choose the correct pair of functions.…

A:

Q: Determine whether the functions f1(x) := x + 1; f2(x) := sin(x); f3(x) := x - 1; f4(x) := 3 are…

A:

Q: f(a + h) – f(a) 7. If f(x) = 3x² +9, find and simplify where h + 0. h За + 6h 3h + 12a ба + 3h 3h +…

A: Hence option (c) is correct.

Q: The functions u and w are defined as follows. u (x) = -2x-1 w (x) = 2x²-2 Find the value of u (w…

A: u(w(3))=-33

Q: Find (g o f)(x) and (fo g)(x) for the given functions f and g. x) - o(x) = Vx-2 x- 2 (go n(x) - (fo…

A: Given: fx=1x2, gx=x-2 To Find: gofxfogx

Q: Find functions f and g so that fo g=H. H(x)=√x² +12 Choose the correct pair of functions. O A. f(x)…

A: We have given a composite function  f○g=H Hx=x2+12 Checking pairs (f○g)x=fgx Afx=x , gx=x2+12…

Q: A homogeneous second-order linear differential equation, two functions y₁ and y₂, and a pair of…

A:

Q: 23. For f(x) = 9x and g(x) = x + 4, find the following functions. a. (fo g)(x); b. (g o f)(x); c. (f…

A: Solution(d) :

Q: Anna and Bob are the only residents of a small town. The town currently funds its fire department…

A: Ans:

Q: -4x + 5 and g(x) K5. Let f(x) a) Determine an equation for the function 2(x) 3D f(x) + g(x). Then,…

A: Given f(x)=-4x2+5 and g(x)=2x-3h(x)=f(x)+g(x)        =-4x2+5+2x-3…

Q: The table below represents the inputs (x) and outputs [f(x), g(x), and h(x)] for three functions.…

A: Answer(a): Given that,  For function f(x), x-values and corresponding f(x) values. Write, these…

Q: Find (f + g)(x), (ƒ − g)(x), (f · g)(x), and (4) (x) for each. 1. f(x) = x² + 4 g(x)=√x 2. f(x) = x²…

A: Given function:- fx=x2+4 ,gx=x fx=x2+x,gx=9x

Q: If f(x) = 2 + 3x – 4x², determine the value of the dependent variable f(5) – f(3). Show your work.

A: We can solve the problem by putting the value 5 and 3 in the given function.

Q: The function f(x) multiplies its input by 6 and then adds 5. Construct a function g(x) that 'undoes'…

A:

Q: 1))Write the equation of a linear function: a) with a slope of 2/3 passing through (6, -1) b)…

A: To write: The equation of linear function  (a) with a slope of 23  and passing through (6, -1) (b)…

Q: . Let f(x) = x2 + x + 3, g(x) = 5x + 3 and h(x) = 2x2 – 4x + 1. Find the following: a. f(4x) b.…

A:

Q: 15. Subtract the functions: f(x)- g(x) where f(x) = -3x + 6 and g(x) = 4x- 2 h(x) = f(x) - g(x) =…

A: Answer and explanation is given below...