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anonymous
 one year ago
Given the function f(x) = log2(x + 6), find the value of f^−1(3).
anonymous
 one year ago
Given the function f(x) = log2(x + 6), find the value of f^−1(3).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I really need help with understanding this.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Answer Choices: a. f−1(3) = 2 b. f−1(3) = 3 c. f−1(3) = 9 d. f−1(3) = 18

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix help please

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SkaterBoyShawn can you help me?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[f^{1}(3)=a \implies f(a)=3 \\ \text{ so you need to solve } \log_2(a+6)=3 \text{ for } a \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles in my notes it was saying how i had to find the inverse function or something like that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me solve it 1sec

freckles
 one year ago
Best ResponseYou've already chosen the best response.2You can find the inverse function then plug in 3 or you can just solve the equation above for a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ugh im still confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think i got the answer

freckles
 one year ago
Best ResponseYou've already chosen the best response.2like why \[f^{1}(3)=a \implies f(a)=3 ? \\ \text{ or on solving } \log_2(a+6)=3 \text{ for } a?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how? @SkaterBoyShawn and @freckles everything like what do you do with log2?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you want to write in the equivalent exponential form

freckles
 one year ago
Best ResponseYou've already chosen the best response.2recall \[\log_b(x)=y \implies b^{y}=x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont get any of this at all. Math is my weakest subject

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so you don't know how to compare \[\log_b(x)=y \text{ to } \log_2(a+6)=3 \\ \text{ then use that } \log_b(x)=y \implies b^y=x \\ \text{ to write } \log_2(a+6)=3 \text{ in exponential form }\]?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433709916685:dw what is in place of the b? in place of the x? in place of the y?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know how to write that in exponential form.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f⁻¹(3) = 2³6 = 2 if u in verse it it i u would get 2^y = x+6 x = 2^y6 f⁻¹(x) = 2ˣ6

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I'm just asking you to identify b,x, and y in that comparison

freckles
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433710114097:dw do you not see that b is 2? can you try to identify what is place of x and y now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i see that now. x is 6 and y is 3.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well x is everything in that log thing so x is a+6 not just 6

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\log_b(x)=y \implies b^y=x \\ \text{ so we can use this to write } \log_2(a+6)=3 \implies 2^{3}=a+6\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2can you solve 2^3=a+6 for a ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y would be f⁻¹(x) = 2ˣ6 not sure yet for b is

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so since f(2)=3 then f^(1)(3)=2

freckles
 one year ago
Best ResponseYou've already chosen the best response.2And I think @SkaterBoyShawn is trying to attempt to find the inverse function and then plug in there instead which is cool too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for problems like that all you have to do is plug in the numbers and solve for a?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[y=\log2(x+6) \\ 2^y=x+6 \\ x=2^y6 \\ f^{1}(x)=2^x6\] his inverse function is right

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so if you have done it this way you can just replace the x with 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do u guys understand the the inverse function

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yeah the function f(x)=log_b(x) is one to one so it does have an inverse function to find something like this: \[f^{1}(3) \] where f^(1) is the inverse of f you could say well I know the following \[f^{1}(3)=a \implies f(a)=3\] so yes in the original you can replace x with a (or just leave the x there if you are feeling lazy) and then solve for a (or x if you left a x instead)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles u understand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay I got it now i think @freckles

freckles
 one year ago
Best ResponseYou've already chosen the best response.2In general: Let's say you have the following problem: \[\text{ Find } f^{1}(m) \text{ if } f(x)=\log_b(x) \\ \\ \text{ assume } f^{1}(m)=a \text{ well this means } f(a)=m \\ \\ \text{ so you replace } x \text{ with } a \text{ like so } \\ f(a)=\log_b(a) \\ \text{ now remember } f(a)=m \\ \text{ so we can replace } f(a) \text{ with } m \\ m=\log_b(a) \\ \text{ and solve for } a \\ b^m=b^{\log_b(a)} \\ b^m=a \\ a=b^m \\ \text{ so remember } a=f^{1}(m) \\ \text{ and that is what we were aiming to find } \\ f^{1}(m)=a=b^m \\ f^{1}(m)=b^m\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2notice the is the inverse function of f(x) evaluated at x=m
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