the inverse function of f(x)=5x-9 and g(x)=(x+5)/9

Question

jdoe0001 · Answer

flip the letters to get the inverse

jdoe0001 · Answer

$\bf f(x)=5x-9 \implies \color{red}{y} =5\color{blue}{x}-9 \qquad \qquad f^{-1}(x) \implies \color{blue}{x} = 5\color{red}{y}-9$

debbieg · Answer

Huh?? no no no.

You do need to write in "y=..." notation, rather than "f(x)". Then you SWITCH the x and the y (although some books may teach is slightly differently, but I'll go with this method for now because I think it is most standard).  That is, you write an x in where the y is, and write in y's for any x's.

THEN you SOLVE for y.

So, for:

$\Large f(x)=5x-9 $ 

you write with a y:
$\Large y=5x-9 $   

Switch the y for x and x for y:
$\Large x=5y-9 $      but THIS is NOT the inverse function.

Now SOLVE for y:

$\Large x+9=5y $

$\Large y=\dfrac{x+9}{5} $

THAT's your inverse:  $\Large f^{-1}(x)=\dfrac{x+9}{5} $

This is usually called the "switch and solve" method.

Now see if you can do it with your other function. :)

anonymous · Answer

thanks DebbieG