Find the value of the function for the given value of x. f(x)={3if 04, for , for x=6.2f(x)=\begin{cases}3 & \text{if }04,\text{ for }\end{cases},\text{ for }x=6.2

Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. 2 - Graphs and Functions

문제 52

3장, 문제 52

Find the value of the function for the given value of x.
$f (x) = {\begin{matrix} 3 & if 0 < x \leq 4 \\ 10 - 2 [[5 - x]] & if x > 4, for \end{matrix}, for x = 6.2$

검증된 단계별 안내

First, carefully read the piecewise function definition to understand the different cases for ƒ(x). It seems the function has different values depending on the value of x.

Identify the value of x given in the problem, which is x = 6.2, and determine which part of the piecewise function applies to this value.

Check the conditions in the piecewise function to see where x = 6.2 fits. For example, if the function is defined as ƒ(x) = 3 for x < 4, and some other value for x ≥ 4, then since 6.2 is greater than 4, you will use the second part of the function.

Once you identify the correct piece of the function for x = 6.2, substitute x = 6.2 into that expression or use the given constant value for that interval.

Write down the value of ƒ(6.2) based on the substitution or the constant value from the piecewise function.

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 Notation and Evaluation

Function notation, written as ƒ(x), represents a rule that assigns each input x to exactly one output. Evaluating a function means substituting the given x-value into the function's rule to find the corresponding output.

Piecewise Functions

A piecewise function is defined by different expressions depending on the input value's domain. Understanding which part of the function applies to the given x-value is essential for correctly evaluating the function.

Domain and Input Values

The domain of a function is the set of all possible input values. Identifying whether the given x-value lies within the domain or specific intervals of a piecewise function helps determine which rule to use for evaluation.

Find the value of the function for the given value of x. f(x)={3if 0<x≤410−2[[5−x]]if x>4, for , for x=6.2f(x)=\(\begin{cases}\)3 & \(\text{if }\)0<x\(\leq\)4\\ 10-2[\(\left\]\lbrack\)5-x]\(\right\[\rbrack\) & \(\text{if }\)x>4,\(\text{ for }\]\end{cases}\),\(\text{ for }\)x=6.2