Question

If f -1(x) = (6/5)x - 9, find f (x).

Answer 1

Solution

Step 1

Write the inverse function:

$f^{-1}(x)\text{ = }\frac{6}{5}x\text{ - 9}$

Step 2

$\begin{gathered} Let\text{ f}^{-1}(x)\text{ = y} \\ \\ y\text{ = }\frac{6}{5}x\text{ - 9} \\ \\ Make\text{ x the subject of the formula} \\ \\ y\text{ + 9 = }\frac{6}{5}x \\ \\ Divide\text{ both sides by }\frac{6}{5} \\ \\ x\text{ = }\frac{5}{6}(y\text{ + 9\rparen} \\ \\ f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen} \end{gathered}$

Final answer

$f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen}$