Question

the following function is one - to - one. find the inverse of the function and graph the function and its inverse on the same set of axes.\\(f(x)=2x - 3\\)\\(f^{-1}(x)=\frac{x + 3}{2}\\) (type a simplified fraction.) use the graphing tool to graph the function and its inverse. click to enlarge graph

Explanation:

Step1: Replace \( f(x) \) with \( y \)

Given \( f(x) = 2x - 3 \), we write \( y = 2x - 3 \).

Step2: Swap \( x \) and \( y \)

Interchange \( x \) and \( y \) to get \( x = 2y - 3 \).

Step3: Solve for \( y \)

Add 3 to both sides: \( x + 3 = 2y \).
Divide both sides by 2: \( y = \frac{x + 3}{2} \).
Replace \( y \) with \( f^{-1}(x) \), so \( f^{-1}(x) = \frac{x + 3}{2} \).

Answer:

The inverse function is \( \boldsymbol{f^{-1}(x) = \frac{x + 3}{2}} \).