Question

Find the inverse function

Answer 1

Answer

${f}^{ - 1} (x) = \frac{5}{2} x - 5.$

Step by step

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

Swap roles of x and y

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

Then

$5x = 2y + 10$

So

$2y = 5x - 10$

Hence

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

Therefore

${f}^{ - 1} (x) = \frac{5}{2} x - 5.$