Question

which of the following is the function f(x) if f^-1(x)=x/8+3a, f(x)=8(x+3)b, f(x)=8(x-3)c, f(x)=8x-3d, f(x)=8x+3

Answer 1

We can see, from the question, that the inverse function of f(x) is given by:

$f^{-1}(x)=\frac{x}{8}+3$

Now, to find f(x), we need to find the inverse function of the given function. To achieve that, we can proceed as follows:

1. Replace x with y as follows:

$\begin{gathered} f^{-1}(x)=y=\frac{x}{8}+3 \\ \\ y=\frac{x}{8}+3\Rightarrow x=\frac{y}{8}+3 \\ \\ x=\frac{y}{8}+3 \end{gathered}$

2. Now, we need to solve the expression for y. First, we need to subtract 3 from both sides of the expression:

$\begin{gathered} x-3=\frac{y}{8}+3-3 \\ \\ x-3=\frac{y}{8} \end{gathered}$

3. We have to multiply both sides of the expression by 8:

$\begin{gathered} 8(x-3)=8(\frac{y}{8})=y \\ \\ 8(x-3)=y \\ \\ y=8(x-3) \end{gathered}$

Therefore, in summary, we have that the function f(x) is as follows:

$f(x)=8(x-3)$

[Option b]