how do i Find the inverse function of f(x), where f(x) = 5x - 3 - 7x + 8?

Question

Find the inverse function of f(x), where f(x) = 5x - 3 - 7x + 8.

Answer 1

f(x) = 5x - 3 - 7x + 8                   Given

f(x) = -2x + 5                             Combine like terms to simplify the expression

y = -2x + 5                                 Substitute y for f(x)

x = -2y + 5                                 Switch x and y

x - 5 = -2y                                  Subtract 5 from each side

(x - 5)/(-2) = y                            Divide each side by -2

y = (5 - x)/2                                Distribute the negative to the numerator to simplify the expression

f^-1(x) = (5 - x)/2                          Replace y with f^-1(x)