1. Solving Functions

Can someone explain how to solve this function please, thanks.

see attachment.

2. $\displaystyle f^{-1}(x)=3\Rightarrow f(f^{-1}(x))=f(3)\Rightarrow x=f(3)$

3. Can someone explain in words what is happening in red dogs explanation please.

4. Originally Posted by red_dog
$\displaystyle f^{-1}(x)=3\Rightarrow f(f^{-1}(x))=f(3)\Rightarrow x=f(3)$
Originally Posted by Tom G
Can someone explain in words what is happening in red dogs explanation please.
What's to explain?

$\displaystyle f^{-1}(x) = 3$<-- Given

$\displaystyle f(f^{-1}(x)) = f(3)$<-- Take the function value of both sides

$\displaystyle f(f^{-1}(x)) = x$<-- By definition

Thus
$\displaystyle x = f(3)$

-Dan

5. Originally Posted by Tom G
Can someone explain in words what is happening in red dogs explanation please.
$\displaystyle f^{-1}(x)=3$

means that $\displaystyle f(3)=x$, that's all there is to it, the inverse
is defined at $\displaystyle x$ so by definition of the inverse of a function $\displaystyle f(3)=x$,

RonL