+0  
 
+2
132
3
avatar

I've been away from school recently due to a nose operation and this monster has appeared in my homework. I understand when there are two equations included, (usually g(x) and h(x). But to find the third, and from what they equal to. If someone could walk me through this I'd heavily appreciate it

 

f(x) = g(h(k(x))) = sin^2(6x) , determine the functions g(x), h(x) and k(x)

Guest Mar 21, 2017
Sort: 

3+0 Answers

 #1
avatar+26251 
+1

One possibility is as follows:

 

\(k(x)=x^{1/2}\\h(x)=6x^2\\g(x)=\sin^2 x\)

 

Note that \(h(k(x))=6(x^{1/2})^2\rightarrow6x\)

.

.

Alan  Mar 21, 2017
edited by Alan  Mar 21, 2017
 #2
avatar
0

How'd you attain these posibilities?? Thanks heaps by the way.

Guest Mar 21, 2017
 #3
avatar+26251 
0

I started by breaking 6x into 6(x1/2)2 and thinking of x1/2 as k, so that h is then 6k2, which leaves g as sin2h.

 

It is not a unique breakdown! For example we could also have k = (6x)1/3, h = x^3, g = sin2x

or an infinite number of other possibilities!

.

Alan  Mar 21, 2017

8 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details