Suppose that the functions p and q are defined as follows.

Question

p(x)=x^2+6

q(x)=√x+9

Find the following

(p·q)(7)

(q·p)(7)

Answer 1

I'm not sure if you mean that the functions should be multiplied or "nested".

I found the word "composition" here:

https://www.mathsisfun.com/sets/functions-composition.html

This is what I call nesting.

If you meant multiplication, then p*q will give the same answer as q*p.....It would simply be:

(x²+6) * (√x+9)

If you meant nesting / composition, then one function has the other function substituted for the variable.

To get p(q(x)), you apply the "p" formula to the expression for q(x):

p(q(x)) = p(√x+9) = (√x+9)² + 6

to get q(p(x)), simply do it the other way around.....

In the reference I cited, they use a small circle to denote composition:

(f º g)(x) = f(g(x))

I have always used the nested notation

Answer 2

I completely agree with the above statement, as that's how I originally read it. However, I just wanted to add something. Please make sure you know if your problem is a multiplication or composition of functions. I.e. is it

(1) (p·q)(7) = p(7)·q(7) or

(2) (pοq)(7) = p(q(7))

As these are two very different problems. The above answer is if your problem is really multiplication. If you folks are studying compositions then the answer would be:

p(x) = x² + 6; q(x) = √x +9

(pοq)(7) = p(q(7))

= p(√7 +9)

= (√7 + 9)² + 6

= 7 + 18√7 + 81 + 6

= 94 + 18√7

(qοp)(7) = q(p(7))

= q(7² + 6) = q(55)

= √55 + 9

As you can see (pοq)(7) ≠ (qοp)(7) <------composite functions usually are not commutative

whereas

(p•q)(7) = p(7)•q(7) = q(7)•p(7) = (q•p)(7) <------multiplying two continuous functions are commutative (which is why the answer above only has one solution).

If you don't know which one your suppose to use, ask your instructor. Ask them to clarify if this problem is a composite function or a multiplication of two functions.

Hope this helps

Mr. K

Answer 3

The way I take it is: (7^2+6)(7^.5+9)=55*(2.645+9)=

55*11.645=640.516