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I really need help with understanding this.

Answer Choices:
a. f−1(3) = 2
b. f−1(3) = 3
c. f−1(3) = 9
d. f−1(3) = 18

@SkaterBoyShawn can you help me?

yes

okay good

\[f^{-1}(3)=a \implies f(a)=3 \\ \text{ so you need to solve } \log_2(a+6)=3 \text{ for } a \]

let me solve it 1sec

You can find the inverse function then plug in 3
or you can just solve the equation above for a

ugh im still confused

i think i got the answer

on what part?

like why \[f^{-1}(3)=a \implies f(a)=3 ? \\ \text{ or on solving } \log_2(a+6)=3 \text{ for } a?\]

how? @SkaterBoyShawn and @freckles everything like what do you do with log2?

you want to write in the equivalent exponential form

recall
\[\log_b(x)=y \implies b^{y}=x\]

i dont get any of this at all. Math is my weakest subject

|dw:1433709916685:dw|
what is in place of the b?
in place of the x?
in place of the y?

i dont know how to write that in exponential form.

f⁻¹(3) = 2³-6 = 2 if u in verse it it i u would get 2^y = x+6
x = 2^y-6
f⁻¹(x) = 2ˣ-6

I'm just asking you to identify b,x, and y in that comparison

i see that now. x is 6 and y is 3.

well x is everything in that log thing
so x is a+6 not just 6

oh okay

can you solve 2^3=a+6 for a ?

a=2

yep

y would be
f⁻¹(x) = 2ˣ-6 not sure yet for b is

so since f(2)=3
then f^(-1)(3)=2

oh okay then

so for problems like that all you have to do is plug in the numbers and solve for a?

\[y=\log2(x+6) \\ 2^y=x+6 \\ x=2^y-6 \\ f^{-1}(x)=2^x-6\]
his inverse function is right

so if you have done it this way you can just replace the x with 3

thank you

do u guys understand the the inverse function

no

no u don't

understand what?

notice the is the inverse function of f(x) evaluated at x=m