Find the value of the function for the given value of x.f(x)={5if 02 , for x=5.6f(x)=\begin{cases}5 & \text{if }02\text{ }\end{cases},\text{ for }x=5.6

Ch. 2 - Graphs and Functions

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Lial 13th Edition

Ch. 2 - Graphs and Functions

문제 51

3장, 문제 51

Find the value of the function for the given value of x.
$f (x) = {\begin{matrix} 5 & if 0 < x \leq 2 \\ 20 - 3 [[2 - 4 x]] & if x > 2 \end{matrix}, for x = 5.6$

검증된 단계별 안내

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

Identify the value of x given in the problem, which is x = 5.6, and determine which part of the piecewise function applies to this value.

Check the conditions for each piece of the function. For example, if the function is defined as ƒ(x) = 5 for some range of x, and another value for a different range, see where 5.6 fits.

Once you find the correct piece of the function that corresponds to x = 5.6, substitute x = 5.6 into that expression or use the constant value given for that interval.

Write down the value of ƒ(5.6) based on the substitution or the constant value from the piecewise function definition.

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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 expression to find the corresponding output.

Piecewise Functions

A piecewise function is defined by different expressions depending on the input value's interval or condition. Understanding which part of the function applies to the given x-value is essential for correct evaluation.

Domain and Conditions in Functions

The domain specifies the set of input values for which the function is defined. Conditions or inequalities often restrict the domain in piecewise functions, guiding which formula to use for a particular x.

Find the value of the function for the given value of x.f(x)={5if 0<x≤220−3[[2−4x]]if x>2 , for x=5.6f(x)=\(\begin{cases}\)5 & \(\text{if }\)0<x\(\leq\)2\\ 20-3[\(\left\]\lbrack\)2-4x]\(\right\[\rbrack\) & \(\text{if }\)x>2\(\text{ }\]\end{cases}\),\(\text{ for }\)x=5.6