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

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Answer 1 · 2018-03-10T20:28:44

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

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

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

$x=3y-5$

$f(y)$ is just the expression $f(x)$ 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 $f^-1(x)$

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

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