# inverse function help

• Jan 6th 2010, 04:21 PM
Corum
inverse function help
f: Dom(f)$\displaystyle \longrightarrow\Re$ , f(x)=$\displaystyle 3-2arccos(\frac{1}{4}x)$

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
• Jan 6th 2010, 04:33 PM
pickslides
To find the inverse you must swap x and y, then solve for y.

Is this what you are after?

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

swapping them over...

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

Now make y the subject.
• Jan 6th 2010, 04:39 PM
Corum
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?
• Jan 6th 2010, 04:41 PM
TKHunny
Quote:

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 $\displaystyle \Re$.
• Jan 6th 2010, 04:43 PM
Corum
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!
• Jan 6th 2010, 04:51 PM
TKHunny
?? The DOMAIN of the arccosine FUNCTION is [-1,1]. That is not the Range.
• Jan 6th 2010, 04:57 PM
Corum
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
• Jan 6th 2010, 05:38 PM
TKHunny
Fair enough. Come back to it when you are ready.
• Jan 6th 2010, 05:42 PM
Corum
Except that it's due in in about 8h. (Worried)