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.

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

Step-by-step 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.