Question

F(x)=x^2+6 and g(x)=2x-1
G[f(x)]=
A.4x^2-4x+7
B.2x^2+11
C.2x^2+5

Answer 1

g( f(x) ) = 2x^2 + 11 (Answer choice B)

Explanation:

g( f(x) ) involves using the function f(x) = x^2 + 6 as the input to g(x).

Here, g(x) = 2x - 1. Replace the x in g(x) by "f(x)" and the x in 2x - 1 by x^2 + 6. Then we have g( f(x) ) = 2[x^2 + 6] -1. This can be simplified, as follows:

= 2x^2 + 12 - 1, or 2x^2 + 11. This is answer choice B.