suppose that the functions p and q are defined as
p(x)=x^2+3
q(x)= squarex+2
(q*p)(2)=
(p*q)(2)=
you will have to define (q*p)(x)
is it the same as q(p(x)) ?
To find the value of (q*p)(2) and (p*q)(2), we need to evaluate the composite functions q(p(x)) and p(q(x)) at x = 2.
First, let's find q(p(x)):
1. Substitute p(x) into q(x):
q(p(x)) = (p(x))^2 + 2
2. Replace p(x) with its definition:
q(p(x)) = (x^2 + 3)^2 + 2
Next, let's evaluate q(p(x)) at x = 2:
1. Substitute x = 2 into q(p(x)):
q(p(2)) = (2^2 + 3)^2 + 2
2. Simplify the expression:
q(p(2)) = (4 + 3)^2 + 2
= 7^2 + 2
= 49 + 2
= 51
Therefore, (q*p)(2) = q(p(2)) = 51.
Now, let's find p(q(x)):
1. Substitute q(x) into p(x):
p(q(x)) = (q(x))^2 + 3
2. Replace q(x) with its definition:
p(q(x)) = (squarex + 2)^2 + 3
Next, let's evaluate p(q(x)) at x = 2:
1. Substitute x = 2 into p(q(x)):
p(q(2)) = (square2 + 2)^2 + 3
2. Simplify the expression:
p(q(2)) = (4 + 2)^2 + 3
= 6^2 + 3
= 36 + 3
= 39
Therefore, (p*q)(2) = p(q(2)) = 39.