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

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

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

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

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

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 $\displaystyle (0,1)$ by $\displaystyle f^{-1}$

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

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

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

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