How do you find the inverse of $g(x)= log_3(x+2)-6$ ?

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Answer 1 · 2015-12-03T15:56:02

$g^-1(x)=3^(x+6)-2$

Write as:

$color(white)(xx)y=log_3(z+2)-6$

Switch $x$ and $y$ .

$color(white)(xx)x=log_3(y+2)-6$

Solve for $y$ .

$color(white)(xx)x+6=log_3(y+2)$

$color(white)(xx)3^(x+6)=3^(log_3(y+2))$

$color(white)(xx)3^(x+6)=y+2$

$color(white)(xx)3^(x+6)-2=y$

Rewrite with $g^-1(x)$ instead of $y$ .

$color(white)(xx)g^-1(x)=3^(x+6)-2$

How do you find the inverse of g(x)= log_3(x+2)-6g(x)= log_3(x+2)-6?