Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

Answer 1

Given:

$f(x)=\dfrac{8}{x}$

$g(x)=\dfrac{8}{x}$

To find:

Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.

Solution:

We know that, two function are inverse of each other if:

$f(g(x))=x$ and $g(f(x))$

We have,

$f(x)=\dfrac{8}{x}$

$g(x)=\dfrac{8}{x}$

Now,

$f(g(x))=f(\dfrac{8}{x})$              $[\because g(x)=\dfrac{8}{x}]$

$f(g(x))=\dfrac{8}{\dfrac{8}{x}}$            $[\because f(x)=\dfrac{8}{x}]$

$f(g(x))=8\times \dfrac{x}{8}$

$f(g(x))=x$

Similarly,

$g(f(x))=f(\dfrac{8}{x})$              $[\because f(x)=\dfrac{8}{x}]$

$g(f(x))=\dfrac{8}{\dfrac{8}{x}}$            $[\because g(x)=\dfrac{8}{x}]$

$g(f(x))=8\times \dfrac{x}{8}$

$g(f(x))=x$

Since, $f(g(x))=x$ and $g(f(x))$, therefore, f(x) and g(x) are inverse of each other.