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

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