Question

For the function f(x)= -5x+2 what is f^-1(x)

Answer 1

this says multiply by -5 then add 2. your inverse will say subtract 2 then divide by -5
\[f^{-1}(x)=\frac{x-2}{-5}\]

Answer 2

a more prosaic but effective way of doing this is to write
\[y=-5x+2\] then switch x and y and write
\[x=-5y+2\] and solve for y. that will be your inverse

Answer 3

\[x=-5y+2\]
\[x-2=-5y\]
\[\frac{x-2}{-5}=y\]

Answer 4

and if you think about it this is just like the elementary algebra question
SOLVE FOR X
\[-5x+2=12\] to do this it is like saying "i know the output, what was the input?" and the steps are identical. now you have a function
\[f^{-1}(x)=\frac{x-2}{-5}\] that does it for you

Answer 5

I don't know how I forgot that. Thank You :)

Answer 6

welcome!