Question

Consider the function.

Answer 1

Answer:

Option 4

Step-by-step explanation:

Given function is,

$f(x)=2\frac{1}{2}-3\frac{1}{3}x$

Steps to get the inverse of the given function,

Step 1,

Convert the function into equation,

$y=2\frac{1}{2}-3\frac{1}{3}x$

Step 2,

Interchange the variables 'x' and 'y',

$x=2\frac{1}{2}-3\frac{1}{3}y$

Step 3,

Solve the equation for the value of y,

$x-2\frac{1}{2}=-3\frac{1}{3}y$

$x-\frac{5}{2}=-\frac{10}{3}y$

$-x+\frac{5}{2}=\frac{10}{3}y$

$-3x+\frac{15}{2}=10y$

$-\frac{3}{10}x+\frac{15}{20}=y$

$y=-\frac{3}{10}x+\frac{3}{4}$

Step 4,

Convert the equation into inverse function,

$f^{-1}x=-\frac{3}{10}x+\frac{3}{4}$

For x-intercepts,

Substitute y = 0,

$0=-\frac{3}{10}x+\frac{3}{4}$

$\frac{3}{10}x=\frac{3}{4}$

$x=\frac{10}{4}$

$x=\frac{5}{2}$

$x=2\frac{1}{2}$

Therefore, x-intercept of the inverse function is $(2\frac{1}{2},0)$.

Option 4 will be the answer.