Question

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

Answer 1

Step 1

Write the inverse function:

`f^(-1)(x)\text{ = }(6)/(5)x\text{ - 9}`

Step 2

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

Final answer

`f(x)\text{ = }(5)/(6)(x\text{ + 9\rparen}`