Question

2. Given the function f(x) = log2(x + 6), find the value of f−1(3).

Answer 1

what do u mean by f-1(3) ? may be something is nor right.

Answer 2

f^-1 (3)

Answer 3

sorry about that

Answer 4

you need to find the inverse function 1st before anything else...

swap x and y and you have

\[x = \log_{2}(y + 6)\]

now make y the subject...

once you have the inverse, just substitute x = 3

hope it helps

Answer 5

Hi, I have no idea how to do that. do you have the time to help me?

Answer 6

Here are the answers and the original question if that helps.

Answer 7

well there is a log law that says

\[a^{\log_{a}(b)} = b\]

which requires you to raise each side of the equation as a power of the base of 2

so

\[2^x = 2^{\log_{2}(y + 6)}\]

so what do you think happens next

Answer 8

Would you try to get rid of the y+6?

Answer 9

well that is what is left, the fact that the base of the exponent and base of the log are the same, the problem becomes

\[2^x = y + 6\]

now solve for y.

that will be the inverse function.

last part to find \[f^{-1}(3)\]

just substitute x = 3 into the function and evlauate

Answer 10

so 8=y+6.
And then what do you do for the f-1(3) part?

Answer 11

you are being asked to find the value of y that makes the equation true

Answer 12

\[y = 2^x - 6~~~or~~~~~f^{-1}(x) = 2^x - 6\]

Answer 13

Ok. none of those are my answer choices though, in the pitcture i posted earlier are the answer choices. Sorry about this, I just do not get this problem at all

Answer 14

@campbell_st

Answer 15

well that is the equation of the inverse function.... you are asked to find the value of the equation when you substitute x = 3.

Answer 16

so make the substitution and get the answer.

Answer 17

so f-1 (3)=2?

Answer 18

@campbell_st

Answer 19

that's correct