Let ƒ(x)=x2+3 and g(x)=-2x+6. Find each of the following. (ƒ+g)(3)

Ch. 2 - Graphs and Functions

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Ch. 2 - Graphs and Functions

문제 11

3장, 문제 11

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ+g)(3)

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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 = 3 by substituting 3 for x: (ƒ+g)(3) = 3^2 - 2(3) + 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 at a specific value means substituting that value into the function's expression and simplifying to find the output.

Function Addition

The sum of two functions, (ƒ + g)(x), is defined by adding their outputs for the same input x. This means (ƒ + g)(x) = ƒ(x) + g(x), combining the expressions before evaluating at a given value.

Substitution and Simplification

To find (ƒ + g)(3), substitute x = 3 into both ƒ(x) and g(x), then add the results. Simplifying the expressions after substitution yields the final numerical value.