Subjects algebra

Composition Functions 9004Ca

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1. **State the problem:** We need to find the value of the composition of functions \( (p \circ q)(-2) \), where \( p(x) = 6x \) and \( q(x) = x + 4 \). 2. **Recall the definition of composition:** The composition \( (p \circ q)(x) \) means \( p(q(x)) \). We first apply \( q \) to \( x \), then apply \( p \) to the result. 3. **Calculate \( q(-2) \):** $$ q(-2) = -2 + 4 = 2 $$ 4. **Calculate \( p(q(-2)) = p(2) \):** $$ p(2) = 6 \times 2 = 12 $$ 5. **Final answer:** $$ (p \circ q)(-2) = 12 $$ This means when you plug \(-2\) into \( q \), then plug that result into \( p \), you get \( 12 \).