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Math  /  Algebra

QuestionSuppose that the functions pp and qq are defined as follows. p(x)=x2+5q(x)=x+7\begin{array}{l} p(x)=x^{2}+5 \\ q(x)=\sqrt{x+7} \end{array}
Find the following. (p⋅q)(2)=(q⋅p)(2)=\begin{array}{l} (p \cdot q)(2)= \\ (q \cdot p)(2)= \end{array}

Studdy Solution

STEP 1

1. We are given two functions: p(x)=x2+5 p(x) = x^2 + 5 and q(x)=x+7 q(x) = \sqrt{x+7} .
2. We need to find the value of (p⋅q)(2) (p \cdot q)(2) .
3. We need to find the value of (q⋅p)(2) (q \cdot p)(2) .

STEP 2

1. Evaluate p(2) p(2) .
2. Evaluate q(2) q(2) .
3. Calculate (p⋅q)(2) (p \cdot q)(2) .
4. Calculate (q⋅p)(2) (q \cdot p)(2) .

STEP 3

Evaluate p(2) p(2) :
p(2)=(2)2+5 p(2) = (2)^2 + 5

STEP 4

Simplify the expression for p(2) p(2) :
p(2)=4+5 p(2) = 4 + 5 p(2)=9 p(2) = 9

STEP 5

Evaluate q(2) q(2) :
q(2)=2+7 q(2) = \sqrt{2 + 7}

STEP 6

Simplify the expression for q(2) q(2) :
q(2)=9 q(2) = \sqrt{9} q(2)=3 q(2) = 3

STEP 7

Calculate (p⋅q)(2) (p \cdot q)(2) :
(p⋅q)(2)=p(2)⋅q(2) (p \cdot q)(2) = p(2) \cdot q(2) (p⋅q)(2)=9⋅3 (p \cdot q)(2) = 9 \cdot 3

STEP 8

Simplify the expression for (p⋅q)(2) (p \cdot q)(2) :
(p⋅q)(2)=27 (p \cdot q)(2) = 27

STEP 9

Calculate (q⋅p)(2) (q \cdot p)(2) :
(q⋅p)(2)=q(2)⋅p(2) (q \cdot p)(2) = q(2) \cdot p(2) (q⋅p)(2)=3⋅9 (q \cdot p)(2) = 3 \cdot 9

STEP 10

Simplify the expression for (q⋅p)(2) (q \cdot p)(2) :
(q⋅p)(2)=27 (q \cdot p)(2) = 27
The values are:
(p⋅q)(2)=27 (p \cdot q)(2) = 27 (q⋅p)(2)=27 (q \cdot p)(2) = 27

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