Question:
Consider the following piecewise definition of the function f.
\(f(x) = \begin{cases} 3-x,\,\,\,if & \quad x≤0\\ x^2 +2,\,if & \quad x≥0 \end{cases}\)
Evaluate f(-3).
Consider the following piecewise definition of the function f.
\(f(x) = \begin{cases} 3-x,\,\,\,if & \quad x≤0\\ x^2 +2,\,if & \quad x≥0 \end{cases}\)
Evaluate f(-3).
\(f(x) = \begin{cases} 3-x,\,\,\,if & \quad x≤0\\ x^2 +2,\,if & \quad x≥0 \end{cases}\)
Evaluate f(-3).
Updated On: Dec 1, 2025
- 6
- 0
- 11
- -7
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The Correct Option is A
Solution and Explanation
To evaluate the function \(f(-3)\) using the given piecewise definition, we first need to determine which part of the function applies to \(x = -3\).
The function \(f(x)\) is defined as:
\[ f(x) = \begin{cases} 3-x, & \text{if } x \leq 0 \\ x^2 + 2, & \text{if } x \geq 0 \end{cases} \]
Since \(-3 \leq 0\), we use the first piece of the function: \(f(x) = 3-x\).
Substitute \(x = -3\) into the expression:
\[f(-3) = 3 - (-3) = 3 + 3 = 6\]
Thus, the value of \(f(-3)\) is 6.
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