QuestionAugust 25, 2025

Evaluate the indicated function for f(x)=x^2-3 and g(x)=x-7 algebraically. (f+g)(1)=square

Evaluate the indicated function for f(x)=x^2-3 and g(x)=x-7 algebraically. (f+g)(1)=square
Evaluate the indicated function for f(x)=x^2-3 and g(x)=x-7 algebraically. (f+g)(1)=square

Solution
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Answer

-8 Explanation 1. Define the combined function (f+g)(x) = f(x) + g(x) 2. Substitute the expressions for f(x) and g(x) (f+g)(x) = (x^2 - 3) + (x - 7) 3. Simplify the expression Combine like terms: x^2 + x - 10 4. Evaluate at x=1 Substitute x=1: 1^2 + 1 - 10 = 1 + 1 - 10 = -8

Explanation

1. Define the combined function<br /> $(f+g)(x) = f(x) + g(x)$<br /><br />2. Substitute the expressions for $f(x)$ and $g(x)$<br /> $(f+g)(x) = (x^2 - 3) + (x - 7)$<br /><br />3. Simplify the expression<br /> Combine like terms: $x^2 + x - 10$<br /><br />4. Evaluate at $x=1$<br /> Substitute $x=1$: $1^2 + 1 - 10 = 1 + 1 - 10 = -8$
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