Question

Consider the function.

f(x)=2 1/2 - 3 1/3
What is the x-intercept of f-1(x)?

o (-3 1/3,0)
o (-3/10,0)
o (3/4,0)
o (2 1/2,0)

Answer 1

Option 4

Explanation:

Given function is,

`f(x)=2(1)/(2)-3(1)/(3)x`

Steps to get the inverse of the given function,

Step 1,

Convert the function into equation,

`y=2(1)/(2)-3(1)/(3)x`

Step 2,

Interchange the variables 'x' and 'y',

`x=2(1)/(2)-3(1)/(3)y`

Step 3,

Solve the equation for the value of y,

`x-2(1)/(2)=-3(1)/(3)y`

`x-(5)/(2)=-(10)/(3)y`

`-x+(5)/(2)=(10)/(3)y`

`-3x+(15)/(2)=10y`

`-(3)/(10)x+(15)/(20)=y`

`y=-(3)/(10)x+(3)/(4)`

Step 4,

Convert the equation into inverse function,

`f^(-1)x=-(3)/(10)x+(3)/(4)`

For x-intercepts,

Substitute y = 0,

`0=-(3)/(10)x+(3)/(4)`

`(3)/(10)x=(3)/(4)`

`x=(10)/(4)`

`x=(5)/(2)`

`x=2(1)/(2)`

Therefore, x-intercept of the inverse function is
`(2(1)/(2),0)`.

Option 4 will be the answer.