## Functions and recurrence relations homework

### Lee1994

Posted 21 September 2010 - 07:45 PM

So... im really stuck and my teacher says she is too busy to help me!
Here goes... functions.
f(x)= 3-x and G(x)= 3/x, X does not equal 0
a Find p(x) where p(x)= f(g(x))
b If q(x)= 3/3-x, x does not equal 3, find p(q(x)) in it's simplest form

Also... recurrence relations.
Two sequences are generated by the recurrence realations un+1= aun + 10 and vn+1= a^2vn + 16
The two sequences approach the same limit as n tends to infinity.
Determine the value of a and evaluate the limit.

Hope someone can understand this. Good luck x

### Physics and Maths Tutor

Posted 24 September 2010 - 11:41 PM

Lee1994, on 21 September 2010 - 07:45 PM, said:

So... im really stuck and my teacher says she is too busy to help me!
Here goes... functions.
f(x)= 3-x and G(x)= 3/x, X does not equal 0
a Find p(x) where p(x)= f(g(x))
b If q(x)= 3/3-x, x does not equal 3, find p(q(x)) in it's simplest form

Also... recurrence relations.
Two sequences are generated by the recurrence realations un+1= aun + 10 and vn+1= a^2vn + 16
The two sequences approach the same limit as n tends to infinity.
Determine the value of a and evaluate the limit.

Hope someone can understand this. Good luck x

a)
p(x) = f(g(x)) = f(3/x)
and f(x) = 3-x
so, f(3/x) = 3-3/x
i.e, p(x) = 3-3/x

b)
p(x) = 3-3/x and q(x) = 3/(3-x)
so, p(q(x)) = p(3/(3-x)) = 3-3/(3/(3-x)) = 3-(3-x) = x

Maths & Physics Tutor Edinburgh
www.physics-maths.co.uk

### Lee1994

Posted 27 September 2010 - 11:37 AM

Physics and Maths Tutor, on 24 September 2010 - 11:41 PM, said:

Lee1994, on 21 September 2010 - 07:45 PM, said:

So... im really stuck and my teacher says she is too busy to help me!
Here goes... functions.
f(x)= 3-x and G(x)= 3/x, X does not equal 0
a Find p(x) where p(x)= f(g(x))
b If q(x)= 3/3-x, x does not equal 3, find p(q(x)) in it's simplest form

Also... recurrence relations.
Two sequences are generated by the recurrence realations un+1= aun + 10 and vn+1= a^2vn + 16
The two sequences approach the same limit as n tends to infinity.
Determine the value of a and evaluate the limit.

Hope someone can understand this. Good luck x

a)
p(x) = f(g(x)) = f(3/x)
and f(x) = 3-x
so, f(3/x) = 3-3/x
i.e, p(x) = 3-3/x

b)
p(x) = 3-3/x and q(x) = 3/(3-x)
so, p(q(x)) = p(3/(3-x)) = 3-3/(3/(3-x)) = 3-(3-x) = x

Maths & Physics Tutor Edinburgh
www.physics-maths.co.uk