Question

46.The function f graphed above is the function f(x) = log2(x) + 2 for x > 0. Find a formula for the inverse of this function.

Answer 1

The inverse for log₂(x) + 2 is - log₂x + 2.

Explanation:

Given that

f(x) = log₂(x) + 2

Now to find the inverse of any function we put we replace x by 1/x.

f(x) = log₂(x) + 2

f(1/x) =g(x)= log₂(1/x) + 2

As we know that

log₂(a/b) = log₂a - log₂b

g(x) = log₂1 - log₂x + 2

We know that log₂1 = 0

g(x) = 0 - log₂x + 2

g(x) = - log₂x + 2

So the inverse for log₂(x) + 2 is - log₂x + 2.