Answer:
Option 4
Step-by-step explanation:
Given function is,
[tex]f(x)=2\frac{1}{2}-3\frac{1}{3}x[/tex]
Steps to get the inverse of the given function,
Step 1,
Convert the function into equation,
[tex]y=2\frac{1}{2}-3\frac{1}{3}x[/tex]
Step 2,
Interchange the variables 'x' and 'y',
[tex]x=2\frac{1}{2}-3\frac{1}{3}y[/tex]
Step 3,
Solve the equation for the value of y,
[tex]x-2\frac{1}{2}=-3\frac{1}{3}y[/tex]
[tex]x-\frac{5}{2}=-\frac{10}{3}y[/tex]
[tex]-x+\frac{5}{2}=\frac{10}{3}y[/tex]
[tex]-3x+\frac{15}{2}=10y[/tex]
[tex]-\frac{3}{10}x+\frac{15}{20}=y[/tex]
[tex]y=-\frac{3}{10}x+\frac{3}{4}[/tex]
Step 4,
Convert the equation into inverse function,
[tex]f^{-1}x=-\frac{3}{10}x+\frac{3}{4}[/tex]
For x-intercepts,
Substitute y = 0,
[tex]0=-\frac{3}{10}x+\frac{3}{4}[/tex]
[tex]\frac{3}{10}x=\frac{3}{4}[/tex]
[tex]x=\frac{10}{4}[/tex]
[tex]x=\frac{5}{2}[/tex]
[tex]x=2\frac{1}{2}[/tex]
Therefore, x-intercept of the inverse function is [tex](2\frac{1}{2},0)[/tex].
Option 4 will be the answer.
