Write an expression for the inverse of
$f (x) = \frac{2}{3} x - 5$
$f^{- 1} (x) =$

Answer

Expert–verified

Hide Steps

Answer

$f^{- 1} (x) = \frac{3}{2} x + \frac{15}{2}$

Steps

Step 1 ：Given function: $f (x) = \frac{2}{3} x - 5$

Step 2 ：Swap x and y: $x = \frac{2}{3} y - 5$

Step 3 ：Solve for y: $y = \frac{3}{2} x + \frac{15}{2}$

Step 4 ： $f^{- 1} (x) = \frac{3}{2} x + \frac{15}{2}$