Question

If F(x) = 2x-7, What is the equation for f^-1(x)

Answer 1

`f^(-1)(x)=(x+7)/(2)`

Step-by-step explanation

Given function:

`f(x)=2x-7`

What to find:

f⁻¹(x)

Step-by-step solution:

`\begin{gathered} \text{Let y }=f(x) \\ \Rightarrow y=2x-7 \\ \text{Make x the subject of the relation} \\ 2x=y+7 \\ x=(y+7)/(2) \end{gathered}`

Since y = f(x), it follows:

`\begin{gathered} x=f^(-1)(y) \\ \text{That is }x=f^(-1)(y)=(y+7)/(2) \\ \end{gathered}`

Hence,

`f^(-1)(x)=(x+7)/(2)`