Question

+3Which of the following is the function f(x) if f'(x) =

Answer 1

f(x) = 8(x -3) (option C)

Step-by-step explanation:

`f^(-1)(x)\text{ = }(x)/(8)+3`

let y = inverse of f(x)

`y\text{ = }(x)/(8)+\text{ 3}`

Interchange x and y:

`\begin{gathered} x=\text{ }(y)/(8)+\text{ 3} \\ mu\text{ltiply through by 8:} \\ 8(x)\text{ = 8}((y)/(8))+\text{ 3(8)} \\ 8x\text{ = y + 24} \end{gathered}`
`\begin{gathered} \text{make y the suject of by subtracting 24 to both sides} \\ 8x\text{ - 24 = y} \\ y\text{ = 8(x - 3) (option C)} \\ f(x)\text{ = 8(x - 3) (option C)} \end{gathered}`