Question

Question 35.Find the inverse of the given function. Graph both functions on the same set of axes and show the line Y=x as a dotted line in the graph.

Answer 1

We have to find the inverse function of f(x):

$f(x)=2x-3$

We can think of the inverse function g(x) as:

$y=g(x)\Rightarrow x=f(y)$

Then, when writing x = f(y) we will get:

$\begin{gathered} x=f(y) \\ x=2y-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{1}{2}x+\frac{3}{2} \end{gathered}$

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