Question

If f(x) =
`(x+3)/(4)`, what is the equation for f–1(x)?

f–1(x) = 4(x + 3)

f–1(x) = 4x - 3

f–1(x) = 4(x - 3)

f–1(x) = 4x + 3

Answer 1

Choice b is correct.

The inverse of function f(x)=x+3/4 is 4x-3

Explanation:

Given function is:

f(x)=x+3 / 4

We have to find the inverse of f(x)

Put f(x)=y in above equation

y = x+3 / 4

We have to separate x from above equation.

Multiplying 4 on both sides of above equation,we have

4y=(x+3)

Adding -3 to both sides of above equation,we have

4y-3=x+3-3

x=4y-3

Replacing y to x and x to f⁻¹(x) we have

f⁻¹(x)=4x-3

This is our required result.

The inverse of the function f(x)=x+3/4 is 4x-3

Answer 2

option (b) is correct

inverse of function
`f(x)=(x+3)/(4)` is 4x+3

Explanation:

Given function
`f(x)=(x+3)/(4)`

We have to find the inverse of given function.

Let f(x) = y then taking inverse both sides, we get

`f^(-1)(y)=f^(-1)(f(x))\\\\\ f^(-1)(y)=x`

Substitute , x and f(x) in given equation, we get,

`f(x)=(x+3)/(4) \Rightarrow ((f^(-1)(y))+3)/(4)`

Now solve for
`(f^(-1)(y))` , we get,

`(f^(-1)(y))+3=4y`

`(f^(-1)(y))=4y-3`

Thus, inverse of function
`f(x)=(x+3)/(4)` is 4x+3

Thus, option (b) is correct.