QuestionJune 5, 2025

Suppose that the functions p and p(x)=x^2+1 Find the following. (qcirc p)(3)= square (pcirc q)(3)= square

Suppose that the functions p and p(x)=x^2+1 Find the following. (qcirc p)(3)= square (pcirc q)(3)= square
Suppose that the functions p and p(x)=x^2+1 Find the following. (qcirc p)(3)= square (pcirc q)(3)= square

Solution
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Answer

(q\circ p)(3)= Cannot be determined without q(x) ### (p\circ q)(3)= Cannot be determined without q(x) Explanation 1. Calculate p(3) Substitute x = 3 into p(x) = x^2 + 1: p(3) = 3^2 + 1 = 9 + 1 = 10. 2. Evaluate (q \circ p)(3) This requires q(p(3)) = q(10). Without q(x), this cannot be completed. 3. Assume q(x) for (p \circ q)(3) Similarly, without q(x), (p \circ q)(3) cannot be evaluated.

Explanation

1. Calculate $p(3)$<br /> Substitute $x = 3$ into $p(x) = x^2 + 1$: $p(3) = 3^2 + 1 = 9 + 1 = 10$.<br />2. Evaluate $(q \circ p)(3)$<br /> This requires $q(p(3)) = q(10)$. Without $q(x)$, this cannot be completed.<br />3. Assume $q(x)$ for $(p \circ q)(3)$<br /> Similarly, without $q(x)$, $(p \circ q)(3)$ cannot be evaluated.
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