f(x) = 3x - 1. g(x) = x + 4. h(x) = x2. Then (h o f)(x) =

Question

these are the answers

	A)  3x + 11
	B)  3x + 3
	C)  4x + 3
	D)  3x2 + 11x - 4
	E)  3x2 - 1
	F)  9x2 - 6x + 1
	G)  none of these

 

Answer 1

f(x) = 3x - 1. g(x) = x + 4. h(x) = x2. Then (h o f)(x) =

We can ignore g(x) above, giving us,

f(x) = 3x – 1, h(x) = x^2. Then (h o f)(x) =

Since (h o f)(x) means h(f(x)), where h(f(x)) is the function h() with f(x) as its argument, then

since h(x) = x^2, then h(f) = f^2, i.e.

h(f(x)) = (f(x))^2 = (3x – 1)^2

h(f(x)) = 9x^2 – 6x + 1.

Comparing the last result with the possible answers given, the correct choice is,

Option F) 9x^2 – 6x + 1