Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.
$(ƒ \circ g) (- 2)$

검증된 단계별 안내

Understand that the notation $(ƒ \circ g)(-2)$ means the composition of functions $ƒ$ and $g$ evaluated at $-2$. This is written as $ƒ(g(-2))$, which means you first find $g(-2)$ and then plug that result into $ƒ$.

Calculate $g(-2)$ by substituting $x = -2$ into the function $g(x) = -x + 3$. So, $g(-2) = -(-2) + 3$.

Simplify the expression for $g(-2)$ to find its value. This will give you the input to use in the next step.

Next, substitute the value you found for $g(-2)$ into the function $ƒ(x) = 2x - 3$. So, calculate $ƒ(g(-2)) = 2 \times g(-2) - 3$.

Simplify the expression for $ƒ(g(-2))$ to find the final value of the composition $(ƒ \circ g)(-2)$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Function Composition

Function composition involves applying one function to the result of another, denoted as (f∘g)(x) = f(g(x)). To evaluate (f∘g)(-2), first find g(-2), then substitute that value into f. This process combines two functions into a single operation.

Evaluating Functions

Evaluating a function means substituting a specific input value into the function's formula and simplifying to find the output. For example, to find g(-2), replace x with -2 in g(x) = -x + 3 and simplify.

Linear Functions

Linear functions have the form f(x) = mx + b, where m and b are constants. Both f(x) = 2x - 3 and g(x) = -x + 3 are linear, meaning their graphs are straight lines and their outputs change at a constant rate with respect to x.

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘g)(−2)(ƒ∘g)(-2)