Question

If f(x) = -2x + 4, then f^-1(x) =

Answer 1

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

Explanation:

Consider the real number y such that f ⁻¹(x) = y

`f^(-1)\left( x\right) =y\Longleftrightarrow f\left( y\right) =x`

We need to find y in order to determine the expression of f ⁻¹(x)

f(y) = x ⇔ -2y + 4 = x

⇔ 4 - x = 2y

⇔ y = (4 - x)/2

`\Longleftrightarrow y=-(x)/(2) +2`