Question

f(x) = 1x – 8. Find f '(x) and its domain.

Answer 1

Given the function,

$f(x)=1x-8$$\text{where f(x)=y}$$\begin{gathered} y=1\cdot x-8 \\ y=x-8 \end{gathered}$

Let us make x the subject of formula,

$\begin{gathered} x=y+8 \\ we\text{ will now replace x as y in the equation,} \\ y=x+8 \end{gathered}$$\begin{gathered} \text{Hence,} \\ f^{-1}(x)=x+8 \end{gathered}$

Hence, f '(x) = x + 8.

Let us now get the domain of the function,

The domain of function is the set of input or argument values for which the function is real and defined.

The domain of the function,

$f^-(x)=x+8\text{ is (-}\infty,\infty)$

Hence, the domain of the inverse function is (-∞ , ∞).