Question

If f(x) = log2 (x + 4), what is f−1(3)?

0

2

4

8

Answer 1

log2 (x+4) = 3
find x from here :)

Answer 2

is it 0?

Answer 3

\(\bf f(x)={\color{blue}{ y}}=log_2({\color{red}{ x}}+4)\qquad inverse\implies {\color{red}{ x}}=log_2({\color{blue}{ y}}+4)\\ \quad \\ \quad \\
\textit{log cancellation rule of }{\color{red}{ a}}^{log_{\color{red}{ a}}\square }=\square \qquad thus\\ \quad \\
x=log_2(y+4)\implies {\color{red}{ 2}}^x={\color{red}{ 2}}^{log_{\color{red}{ 2}}(y+4)}\implies {\color{red}{ 2}}^x=y+4\)

Answer 4

solve for "y" and plug in the "3"

Answer 5

is it 4 then? @jdoe0001

Answer 6

well... what did you get for the inverse?

Answer 7

I don't know how to do this, I'm just trying to narrow it down.

Answer 8

well, that's the idea.... that you understand it, thus the exercise

Answer 9

In the inverse function, all the ordered pairs are reversed. If 3 is an x value of the inverse function, that means it was a y value in the function.

Answer 10

That is what hartnn was trying to show you. Take the function and replace y with 3

Answer 11

\[\log_{2}(x+4)=3 \]

Answer 12

yeap

Answer 13

Now put it into its exponential form

Answer 14

\[2^3=x+4\]

Answer 15

@tornjeansxo have youj covered inverse functions yet?

Answer 16

I learned all of this but forgot. It was a few months ago so :/

Answer 17

So we see that x = 4 and (4,3) is an ordered pair of the original function. Therefore (3,4) is an ordered pair of the inverse function and:
\[f ^{-1}(3)=4\]

Answer 18

thank you, guys :)

Answer 19

yw