How do you find the inverse of f(x)=3x-5f(x)=3x5 and is it a function?

1 Answer
Mar 10, 2018

f^-1(x) = (5+x)/3f1(x)=5+x3

Explanation:

The inverse of a function f(x)f(x) is another function, f^-1(x)f1(x), which reverses f(x)f(x). (So yes it is a function)

We can find it by first writing out the equation x=f(y)x=f(y)

x=3y-5x=3y5

f(y)f(y) is just the expression f(x)f(x) but with y's instead of x's

Rearrange to make y the subject (isolate y to be on its own)

In this case, add 5 to both sides and divide both sides by 3

y=(5+x)/3

Finally, replace y with f^-1(x)

f^-1(x) = (5+x)/3