MHB Compositions, Inverses and Combinations of Functions

[mak23]

HELP!

given p(q(x))=2/(5+x) and q(x)=1+x . find a formula for p(x).

Someone please help. I don't know how to do this problem .Thanks in advance
(PS: would be really helpful if solution is also given)

 

[Greg]

Hi mak23,

Since the denominator of p(x) contains the only instance of x, let's define a new function f(q(x)) = f(1 + x) = 5 + x.
So we start with our function f(x) and replace each instance of x with 1 + x. What is our original function f(x)?

Does that help?

 

[mak23]

Hi greg1313,

Thanks for replying to my post. I'm really terrible in this chapter. If u could explain step by step, I would understand much better and quickly. I'm sorry if I'm troubling u.

 

[Greg]

No problem. :)

Here's a hint: a + 1 + x = 5 + x. What is a? What, then, is p(x)?

 

[mak23]

ahaaa...Now i get it..

So p(x)=2/(4+x)

Thank you so much greg1313 for the help!