Question

NEED HELP ASAP PLEASE!!

Answer 1

Option D:

$y=\frac{5x-2}{x}$

Solution:

Given function:

$y=\frac{-2}{x-5}$

To find the inverse of the function.

Inverse of a function:

If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back to x.

$y=\frac{-2}{x-5}$

Interchange the variables x and y.

$x=\frac{-2}{y-5}$

Now, solve for y.

Multiply both sides by (y - 5).

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

Cancel the common factors, we get

$x(y-5)=-2$

Divide by x on both sides.

$y-5=-\frac{2}{x}$

Add 5 on both sides.

$y=-\frac{2}{x}+5$

$y=-\frac{2}{x}+\frac{5}{1}$

To make the denominator same, multiply the 2nd term by $\frac{x}{x}$.

$y=-\frac{2}{x}+\frac{5x}{x}$

$y=\frac{-2+5x}{x}$

$y=\frac{5x-2}{x}$

Option D is the correct answer.