Question

How do I solve and what would the answer be?

Answer 1

Given:

The function is given as,

$f(x)=\frac{2}{x-5}$

The objective is to find the inverse function.

Explanation:

The given expression can be written as,

$y=\frac{2}{x-5}\text{ . . . . . (1)}$

The inverse of a function can be calculated by interchanging the x and y variables in equation (1).

$x=\frac{2}{y-5}\text{ . . . . . (2)}$

Now, solve for y in equation (2).

$\begin{gathered} x(y-5)=2 \\ y-5=\frac{2}{x} \\ y=\frac{2}{x}+5 \end{gathered}$

Hence, the inverse function is y = (2/x) + 5.