Question

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

f−1(3) = 7

f−1(3) = 12

f−1(3) = 23

f−1(3) = 31

Answer 1

\(\Large f(x) = \log_3(x+4)\) ?

Answer 2

yes

Answer 3

In y = f(x), to evaluate, y when x = 3, you would put x = 3 in f(x) and calculate y.
But to to calculate f^-1(3), you set y = 3 and solve for x.
Set x = each answer choice in f(x) and see which one gives you 3.

Answer 4

\(\Large f(x) = \log_3(x+4) \)
\(\Large f^{-1}(3) ~~\text{ means } ~~~3 = \log_3(x+4)\)

Try each answer choice for x and see which one gives 3.

Answer 5

\( \Large
3 = \log_3(x+4) \\ \Large
3^3 = x + 4 \\ \Large
27 = x + 4 \\ \Large
x = 23 \\ \Large
f^{-1}(3) = 23
\)

Answer 6

Thankyou!!