p(x)=2x-2
q(x)=x^2+1
find
(qop)(5)=
(poq)(5)=
q of p = p^2 + 1 = (2x-2)^2 +1 = 4(x^2-2x+1) +1 = 4x^2 -8x + 5
if x = 5
100 - 40 + 5 = 65
You can do the reverse one now.
I interpret (qop)(5)
as (q follows p)(5)
p(5) = 2(5)-2 = 8
q(8) = 8^2 + 1 = 65
so (qop)(5) = 65
Do the 2nd one in the same way
To find (q o p)(5), we need to perform the composition of functions q and p, and then evaluate the resulting function at x = 5.
Step 1: Find q o p
(q o p)(x) means we first apply function p(x) to x, and then apply function q(x) to the output of p(x).
To do this, we substitute p(x) = 2x - 2 into q(x):
(q o p)(x) = q(p(x)) = q(2x - 2) = (2x - 2)^2 + 1
Step 2: Evaluate at x = 5
To find (q o p)(5), we substitute x = 5 into the expression we obtained in Step 1:
(q o p)(5) = (2*5 - 2)^2 + 1
= (10 - 2)^2 + 1
= 8^2 + 1
= 64 + 1
= 65
Therefore, (q o p)(5) = 65.
Now, let's find (p o q)(5):
Step 1: Find p o q
(p o q)(x) means we first apply function q(x) to x, and then apply function p(x) to the output of q(x).
To do this, we substitute q(x) = x^2 + 1 into p(x):
(p o q)(x) = p(q(x)) = p(x^2 + 1) = 2(x^2 + 1) - 2
Step 2: Evaluate at x = 5
To find (p o q)(5), we substitute x = 5 into the expression we obtained in Step 1:
(p o q)(5) = 2((5)^2 + 1) - 2
= 2(25 + 1) - 2
= 2(26) - 2
= 52 - 2
= 50
Therefore, (p o q)(5) = 50.