Let g(x) = f^-1(x), the inverse of function f. Write the rule for for g(x) for each function f.

Question

a. f(x) = (1/4)^x

b. f(x) = 5x - 2

Answer 1

a.

f(x) = (1/4)^x

ln( f(x) ) = ln (1/4)^x

ln( f(x) ) = x * ln (1/4)

x = ln( f(x) ) / ln (1/4)

x = log_1/4f(x)

So g(x) = log_1/4x

b.

f(x) = 5x - 2

f(x) + 2 = 5x

x = ( (f(x) + 2 ) / 5

So g(x) = (x + 2) / 5