Which value is in the domain of [tex]f(x)[/tex]?
[tex]f(x)=\left\{\begin{array}{ll}
2 x+5, & -6\ \textless \ x \leq 0 \
-2 x+3, & 0\ \textless \ x \leq 4
\end{array}\right.[/tex]
A. -7
B. -6
C. 4
Answer (2)
The function f ( x ) is defined piecewise for different intervals of x .
Check if − 7 is in the domain: − 7 is not greater than − 6 , so it's not in the domain.
Check if − 6 is in the domain: − 6 is not strictly greater than − 6 , so it's not in the domain.
Check if 4 is in the domain: 4 satisfies 0 < x ≤ 4 , so it's in the domain. The final answer is 4 .
Explanation
Understanding the Problem We are given a piecewise function f ( x ) and asked to determine which of the values − 7 , − 6 , and 4 is in the domain of f ( x ) . The domain is the set of all possible values of x for which the function is defined.
Defining the Function The function is defined as: f(x)=\left{\begin{array}{ll} 2 x+5, & -6
The only value in the domain of the function f ( x ) is 4 . Values − 7 and − 6 do not satisfy the conditions of the defined intervals. Therefore, the chosen option is C. 4 .
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