Given the function f (x) = log3 (x + 4), find the value of f-1 (3

First of all, find f ⁻¹ (x), or the inverse function like so:

y = log (3x + 12)

e^y = 3x + 12

3x = e^y - 12

x = 1/3 (e^y - 12)

Now, swap x and y:

f ⁻¹ (x) = y = 1/3 (e^x - 12)

Secondly and finally, substitute 3 into this eq'n:

f ⁻¹ (3) = 1/3 (e³ - 12) = 2.695 ...

so 2.695 (to 4 sig. figs / 3 d. ps)

or if asked for an exact answer then it is just: 1/3 (e³ - 12), which can be simplfied to 1/3e³ - 4.