Let ƒ(x)=x2+3ƒ(x)=$$x^2+3 $$and g(x)=−2x+6g(x)=-2x+6. Find each of the following. See Example 1.(ƒ+g)(−5)(ƒ+g)(-5)

Ch. 2 - Graphs and Functions

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Lial 13th Edition

Ch. 2 - Graphs and Functions

문제 12

3장, 문제 12

Let $ƒ (x) = x^{2} + 3$ and $g (x) = - 2 x + 6$ . Find each of the following. See Example 1.
$(ƒ + g) (- 5)$

검증된 단계별 안내

Understand that (ƒ+g)(x) means you add the functions ƒ(x) and g(x) together, so (ƒ+g)(x) = ƒ(x) + g(x).

Write the expressions for ƒ(x) and g(x): ƒ(x) = x^2 + 3 and g(x) = -2x + 6.

Add the two functions together: (ƒ+g)(x) = (x^2 + 3) + (-2x + 6).

Simplify the expression by combining like terms: (ƒ+g)(x) = x^2 - 2x + (3 + 6).

Evaluate the simplified expression at x = -5 by substituting -5 for x: (ƒ+g)(-5) = (-5)^2 - 2(-5) + 9.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output. Evaluating a function means substituting a specific value for x and calculating the result. For example, ƒ(-5) means replacing x with -5 in the function ƒ(x).

Function Addition

The sum of two functions (ƒ + g)(x) is defined as ƒ(x) + g(x). To find (ƒ + g)(-5), evaluate each function at -5 separately, then add the results. This operation combines the outputs of both functions for the same input.

Polynomial and Linear Functions

ƒ(x) = x² + 3 is a polynomial function of degree 2, and g(x) = -2x + 6 is a linear function. Understanding their forms helps in correctly substituting values and performing arithmetic operations on their outputs.

Let ƒ(x)=x2+3ƒ(x)=x^2+3 and g(x)=−2x+6g(x)=-2x+6. Find each of the following. See Example 1.(ƒ+g)(−5)(ƒ+g)(-5)