We have to find the inverse function of f(x):
[tex]f(x)=2x-3[/tex]
We can think of the inverse function g(x) as:
[tex]y=g(x)\Rightarrow x=f(y)[/tex]
Then, when writing x = f(y) we will get:
[tex]\begin{gathered} x=f(y) \\ x=2y-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{1}{2}x+\frac{3}{2} \end{gathered}[/tex]
We know can graph both equation as:
NOTE: we can see in the graph that both functions are reflection of each other across the axis y = x.
Answer: the inverse function of f(x) is (1/2)*x+3/2
