Question

I have to find the inverse function on these and Im so confused - how do I do them?
ease explain:
f^-1(6)=-8 find f(-8)

Answer 1

I have steps 1 - write in y=f(x)
2- solve the equation in step 1 for x in terms of y
3 - interchange x and y in the equation in step 2

Answer 2

\(\bf f(\textit{some domain}) = \textit{some range}\\ \quad \\
f^{-1}(\textit{some range}) = \textit{some domain}\\ \quad \\
f^{-1}(6) = -8\\ \quad \\
f(8) = \square ?\)

Answer 3

-8?

Answer 4

:)

Answer 5

the range of the function, is the domain of its inverse

the domain of its inverse, is the range of the functoin

Answer 6

what happens to the 6?

Answer 7

ohh smokes.. I ... right you said .hmm heheh -8 well no :|
anyhow.. the idea is that

Answer 8

its not -8?

Answer 9

say... lemme give you an example
\(\bf f(x)= 2x+3\qquad \qquad f^{-1}(x) = \cfrac{x-3}{2}\\ \quad \\
f(\color{red}{5}) = 2(5)+3\implies \color{blue}{13}\qquad \qquad f^{-1}(\color{blue}{13})=\cfrac{(13)-3}{2}\implies \cfrac{10}{2}\implies \color{red}{5}\)

Answer 10

so \(\bf f(\textit{some domain}) = \textit{some range}\\ \quad \\
f^{-1}(\textit{some range}) = \textit{some domain}\\ \quad \\
f^{-1}(6) = -8\\ \quad \\
f(8) = \square ?\)

Answer 11

6?

Answer 12

:)

Answer 13

really?! this makes my head hurt. ... so that doesn't change .... I don't get it =(

Answer 14

if you give a value to "x" in the function, any value

then "y" will become, whatever the function spits out

if you give whatever the function spit out, as a value to "x" IN THE INVERSE
the inverse function will spit out, the original value given to the ORIGINAL function

Answer 15

ohhhh! f^-1 is 6 and when y=f(x) the 6 would go where the (x) is?

Answer 16

yeap

Answer 17

yay got it! . I hope! thank you

Answer 18

yw