Question

5. g(x) = x² - 9
find the inverse

Answer 1

This function has domain

$D=\mathbb{R}$

but it can be inverted only in one of the two sub-domains

$D_1=\{x \in \mathbb{R}\ :\ x\geq0\},\quad D_2=\{x \in \mathbb{R}\ :\ x\leq0\}$

In fact, if we invert the function we have

$y=x^2-9\mapsto x=y^2-9 \iff y^2=x+9 \iff y=\pm\sqrt{x+9}$

And you choose the $\pm$ sign depending on which subdomain you're in.

Answer 2

Yo sup??

g(x)=x²-9

y=x²-9

y+9=x²

x=√(y+9)

g-1(x)=√(y+9)

Hope this helps