Question

Which function below is the inverse of f(x) = The quantity of four x minus three, over two. ? (1 point)

Answer 1

The inverse of f(x) is

`f^(-1) (x) = (2 x+3)/(4)`

Explanation:

Explanation:-

Given
`f(x) = (4 x-3)/(2)`

Inverse of f(x)

f(x) is a one-one function

let f(x₁) and f(x₂) be two functions are

`f(x_(1) ) = (4 x_(1) -3)/(2)`

`f(x_(2) ) = (4 x_(2) -3)/(2)`

⇒
`(4 x_(1) -3)/(2) = (4 x_(2) -3)/(2)`

⇒ 4 x₁ - 3 = 4 x₂ - 3

⇒ 4 x₁ = 4 x₂

⇒ x₁ = x₂

Given function is one-one function

y = f(x) =
`(4 x-3)/(2)`

⇒ 2 y = 4 x - 3

⇒ 4 x = 2 y + 3

⇒
`x = (2 y + 3)/(4)`

⇒ f⁻¹(x)
`= (2 y + 3)/(4)`

Given function f(x) is onto function

Therefore f(x) is one-one and onto function

`f^(-1) (x) = (2 x+3)/(4)`