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)=(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=(x)/(8)+3 \\ \\ y=(x)/(8)+3\Rightarrow x=(y)/(8)+3 \\ \\ x=(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=(y)/(8)+3-3 \\ \\ x-3=(y)/(8) \end{gathered}`

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

`\begin{gathered} 8(x-3)=8((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]