We want to determine whether the given pair of functions are .
$f(x)=2x−5 andg(x)=41 x_{2}−5 $
To do so, we need to verify that the compositions of $f(x)$ and $g(x)$ are the *identity function*. Since $g(x)$ is a , we first need to find the , which only includes values for which the radicand is non-negative.
$x−5≥0⇔x≥5 $
Since the domain of $g(x)$ is all real numbers greater than or equal to $5$, we will only consider them for the $x-$variable.

### Calculating $f(g(x))$

To find the expression for

$f(g(x))$ we will start by substituting

$41 x_{2}−5$ for

$g(x).$
$f(g(x))⇒f(41 x_{2}−5)$
Now we apply the definition of

$f(x).$
$f(x)=2x−5 ⇓f(41 x_{2}−5)=241 x_{2}−5−5 $
Finally, let's simplify and see if the function is the

*identity function.*
$f(g(x))=241 x_{2}−5−5 $

$f(g(x))=241 x_{2}−10 $

Since

$f(g(x))$ is

**not** the identity function,

$f(x)$ and

$g(x)$ are

**not** inverse functions.