If $g(x)$ is the inverse of $f(x)$ and $f(x)=4x+ 12$ , what is $g(x)$ ?

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Answer 1 · 2016-04-28T14:45:36

$g(x)=x/4-3$

set $y=4x+12$

subtract 12 from both sides

$y-12=4x$

Divide both sides by 4

$x=y/4-12/4$

$x=y/4-3$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Where there is a $x$ write $y$
Where there is a $y$ write $x$

Giving

$y=x/4-3$

$g(x)=x/4-3$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The inverse function is the original equation reflected about $y=x$

Tony B

If g(x)g(x) is the inverse of f(x)f(x) and f(x)=4x+ 12f(x)=4x+ 12, what is g(x)g(x)?