Question

Given f(x)=-3x+8, find f^-1(x) then state wheter F^-1 (x) is a function

Answer 1

f⁻¹(x) = (8-x)/3 and it is a Function.

Explanation:

Given is f(x) = -3x+8

Suppose y = f(x), then y = -3x + 8

Solving for x:-

-3x + 8 = y

-3x = y - 8

3x = 8 - y

x = (8-y)/3

Now interchanging x and y:-

y = (8-x)/3

Here, y is inverse function i.e. f⁻¹(x)

Hence, f⁻¹(x) = (8-x)/3

Since f⁻¹(x) is a linear expression of x, therefore it is a function.