Question

Given: F(x) = 5x - 6 and G(x) = x - 4

Answer 1

Answer:

Correct choice is $\dfrac{x+26}{5}$

Step-by-step explanation:

1. If $F(x)=5x-6,$ then you can find the inverse $F^{-1}(x):$

$y=5x-6,\\ \\5x=y+6,\\ \\x=\dfrac{y+6}{5},\\ \\F^{-1}(x)=\dfrac{x+6}{5}.$

2. If $G(x)=x-4,$ then

$y=x-4,\\ \\x=y+4,\\ \\G^{-1}(x)=x+4.$

3. Hence,

$G^{-1}(F^{-1}(x))=G^{-1}\left(\dfrac{x+6}{5}\right)=\dfrac{x+6}{5}+4=\dfrac{x+26}{5}.$