Question

3. If f(x)= 3x+ 2 , what is the equation for f^-1(x)

Answer 1

option 3 ⇒ f⁻¹(x) =
`(x^(2) -2 )/(3)`

Explanation:

Given F(x) =
`√(3x+2)`

let y = f(x)

y =
`√(3x+2)` ⇒ squaring the both sides

y² = 3x + 2 ⇒ subtract 2 from both sides

y² - 2 = 3x ⇒ divide both sides by 3

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

replace the location of x and y

∴ y =
`(x^(2) -2 )/(3)`

So, y will be f⁻¹(x)

∴ f⁻¹(x) =
`(x^(2) -2 )/(3)`