Question

use composition to determine if G(x) or H(x) is the inverse of F(x) across the domain x≥-7*PHOTO*

Answer 1

SOLUTIONS

Use composition to determine if G(x) or H(x) is the inverse of F(x) across the domain x≥-7

$\begin{gathered} f(x)=\sqrt{x+7} \\ g(x)=(x-7)^2 \\ h(x)=x^2+7 \end{gathered}$

The inverse of the function of f(x) is

$\begin{gathered} f(x)=\sqrt{x+7} \\ y=\sqrt{x+7} \\ square\text{ both side} \\ y^2=x+7 \\ replace\text{ x = f\lparen x\rparen and y = x} \\ x^2=y+7 \\ x^2-7=y \end{gathered}$

Hence the inverse of the function

$y=x^2-7$

Neither of the function of the f(x) is inverse

Option B