Answer
[tex]f^{-1}(x)=\frac{x+7}{2}[/tex]
Explanation
Given function:
[tex]f(x)=2x-7[/tex]
What to find:
f⁻¹(x)
Step-by-step solution:
[tex]\begin{gathered} \text{Let y }=f(x) \\ \Rightarrow y=2x-7 \\ \text{Make x the subject of the relation} \\ 2x=y+7 \\ x=\frac{y+7}{2} \end{gathered}[/tex]
Since y = f(x), it follows:
[tex]\begin{gathered} x=f^{-1}(y) \\ \text{That is }x=f^{-1}(y)=\frac{y+7}{2} \\ \end{gathered}[/tex]
Hence,
[tex]f^{-1}(x)=\frac{x+7}{2}[/tex]
