Problem Page Suppose that the functions q and r are defined as follows. Q(X)=3X+3; R(X)=-3X-4 Find the following. (Q*R)(-5), (R*Q)(-5)

Question

COMPOSITION OF TWO FUNCTIONS 

Answer 1

If q(x)=x+b
and r(x)= x+d
Then q(r(x)) = (x+d)+b

 

Saying this outloud always helps. You're trying to find Q of (R of -5), so you need to find R of -5 first.

 

(Q*R)(-5):

R(-5) = -3*(-5) - 4
R(-5) = 15 - 4
R(-5) = 11

 

Now plug 11 into the Q function:

Q(X)=3X+3

Q(11) = 3*11 + 3
Q(11) = 33 + 3
Q(11) = 36

 

So, (Q(R(-5)) = 36

 

(R*Q)(-5):
Now you're finding "R of (Q of -5)" so first you must calculate Q(-5).

 

Q(X)=3X+3

Q(-5) = 3*(-5) + 3
Q(-5) = -15 + 3
Q(-5) = -12

 

Now, plug -12 into R(X):
R(X)=-3X-4
R(-12) = -3(-12) - 4
R(-12) = 36 - 4
R(-12) = 32

So, R(Q(-5)) = 32