1. ## inverse function help

f: Dom(f) $\longrightarrow\Re$ , f(x)= $3-2arccos(\frac{1}{4}x)$

Characterize the inverse function of f.
i'm lost on this. characterize cosine? what falls under "characterize"?
I am very grateful for help in solving this

2. To find the inverse you must swap x and y, then solve for y.

Is this what you are after?

$y= 3-2\arccos\left(\frac{1}{4}x\right)$

swapping them over...

$x= 3-2\arccos\left(\frac{1}{4}y\right)$

Now make y the subject.

3. If you invert cos, you get arccos, and vice-versa. that process is how you first arrive at arccos. So graphically that's simple. start from 3, lower concavity. But to characterize? domain? derivative?

4. Originally Posted by Corum
what falls under "characterize"?
Attrributes, properties, characteristics, descriptions.

Minimum value?
Maximum value?
Domain?
Range?
Odd or Even?
Algebraic, Trigonometric, Transcendental?
Useful in finance?
Makes pretty pictures?

What can you say about it?

Try to remember that the Range of the arccosine FUNCTION is NOT $\Re$.

5. the range is [-1,1], seeing as cos is [0,PI]..? i got that the right way round? It does make a nice picture actually, especially in this nice crayon.. thanks for that, just about sums it all up!

6. ?? The DOMAIN of the arccosine FUNCTION is [-1,1]. That is not the Range.

7. sorry, i meant domain. the 40th hour has just struck that i've been working on this non-stop... nothing i say can be payed attention to

8. Fair enough. Come back to it when you are ready.

9. Except that it's due in in about 8h.