1. ## inverse function questions

Hi, I want to learn inverse functions. And I find a problem can you help me to solve this problems ?

2. Basically, if you have $f(x)$ as $x \rightarrow f(x)$, then $f(x)^{-1}$ is $f(x) \rightarrow x$.
The first one is pretty straightforward : you are asked to find $f(1)^{-1}$ when $f(x) = x^2$.

Say $f(x) = y$, you have $y = x^2$. Express $x$ in terms of $y$, thus $x = \sqrt{y}$ or $x = - \sqrt{y}$. Therefore, $f(x)^{-1} = \sqrt{x}$ or $- \sqrt{x}$. Substitute : $f(1)^{-1} = 1$ or $-1$

I don't get b), though, what do you mean by the interval ?

3. Originally Posted by Bacterius
Basically, if you have $f(x)$ as $x \rightarrow f(x)$, then $f(x)^{-1}$ is $f(x) \rightarrow x$.
The first one is pretty straightforward : you are asked to find $f(1)^{-1}$ when $f(x) = x^2$.

Say $f(x) = y$, you have $y = x^2$. Express $x$ in terms of $y$, thus $x = \sqrt{y}$ or $x = - \sqrt{y}$. Therefore, $f(x)^{-1} = \sqrt{x}$ or $- \sqrt{x}$. Substitute : $f(1)^{-1} = 1$ or $-1$

I don't get b), though, what do you mean by the interval ?
I don't know I research everywhere but I didn't find anything about interval in inverse function

4. hi
for (b) u should find the interval image of $(0,1)$ by $f^{-1}$

5. Originally Posted by Raoh
hi
for (b) u should find the interval image of $(0,1)$ by $f^{-1}$
and that depends on $f^{-1}$,
if $f^{-1}$ is increasing the interval image must be $(f^{-1}(0),f^{-1}(1))$.
if $f^{-1}$is decreasing the interval must be $(f^{-1}(1),f^{-1}(0))$.
hope that's right..

6. Originally Posted by Raoh
and that depends on $f^{-1}$,
if $f^{-1}$ is increasing the interval image must be $(f^{-1}(0),f^{-1}(1))$.
if $f^{-1}$is decreasing the interval must be $(f^{-1}(1),f^{-1}(0))$.
hope that's right..
thank you Raoh , can you help for ii) ?

7. for ii) is it $g(x)= \left |x \right |$ ?

8. I don't think so, his function is the floor function, not the absolute value function ...