Question

Given the function f(x) = 3x, find the value of f−1(81).

Answer 1

Given the function f (x) = 3x, find the value of f-1 (81).
 For this case, the first thing you should do is rewrite the function.
 We have then:
 y = 3 ^ x
 From here, we clear the value of x:
 log3 (y) = log3 (3 ^ x)
 log3 (y) = x
 Then, we rewrite the function again:
 f (x) ^ - 1 = log3 (x)
 Now, we evaluate the inverse function for x = 81:
 f (81) ^ - 1 = log3 (81)
 f (x) ^ - 1 = 4
 Answer:
 the value of f-1 (81) is: 
 f (x) ^ - 1 = 4