Answer to Question #235353 in Calculus for CCW

Question

1. (3.) Using the definition of an inverse, are f(x) and g(x) inverses of one another? Why or why not?

Answer 1

Let consider these function

Let

$f(x)=\frac{x+3}{2}$

$g(x)=2x-3$

If function $f(x)$ and $g(x)$ are inverses, their composition will equal $x$

Composition 1:

$f(g(x))=f(x)=\frac{(2x+3)+3}{2}=\frac{2x}{2}=x$

Composition 2:

$g(f(x)) =2(\frac{x+3}{2})-3=x+3-3=x$

Hence these are inverse as their compositions equal x.