What is the inverse of the function $y = 2x + 5$ ?

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Answer 1 · 2016-01-02T14:43:28

If $f(x)=2x+5$
$f(x)^-1=(x-5)/2$

This method works, but I'm not sure how sound it is mathematically.

Let $f(x)=y$
so $y=2x+5$
then rearrange for $x$
so $x=(y-5)/2$
Now swap the subject for $f(x)^-1$ and the $y$ for $x$ .
$f(x)^-1=(x-5)/2$

You can check the answer by substituting in a value for $x$ , example $x=3$

$f(3)=6+5=11$
Then put the answer of that into the inverse equation, and you should receive the first number you put in.

$f(11)^-1=(11-5)/2=6/2=3$

What is the inverse of the function y = 2x + 5y = 2x + 5?