Question
If \( f(x) \) is defined as follows, find (a) \( f(-1) \), (b) \( f(0) \), and (c) \( f(1) \). \( f(x)=\left\{\begin{array}{ll}x^{2} & \text { if } x<0 \\ 3 & \text { if } x=0 \\ 2 x+1 & \text { if } x>0\end{array}\right. \) (a) \( f(-1)=1 \) (Simplify your answer.) (b) \( f(0)=\square \) (Simplify your answer.)
Ask by Frank Bob. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) \( f(-1) = 1 \)
(b) \( f(0) = 3 \)
Solution
The function is defined piecewise as follows:
• If x < 0, then f(x) = x².
• If x = 0, then f(x) = 3.
• If x > 0, then f(x) = 2x + 1.
(a) For f(−1):
Since −1 < 0, we use the rule f(x) = x².
f(−1) = (−1)² = 1.
(b) For f(0):
Since x = 0, we use the rule f(x) = 3.
f(0) = 3.
(c) For f(1):
Since 1 > 0, we use the rule f(x) = 2x + 1.
f(1) = 2(1) + 1 = 3.
Thus, the answers are:
(a) f(−1) = 1
(b) f(0) = 3
(c) f(1) = 3
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Simplify this solution Mind Expander
To solve for the values of \( f(-1) \), \( f(0) \), and \( f(1) \): (a) For \( f(-1) \), since \(-1 < 0\), we use the first piece of the function: \[ f(-1) = (-1)^2 = 1. \] (b) For \( f(0) \), we see that when \( x = 0 \), we use the second piece: \[ f(0) = 3. \] (c) For \( f(1) \), as \( 1 > 0\), we use the third piece of the function: \[ f(1) = 2(1) + 1 = 3. \] So the answers are: (a) \( f(-1) = 1 \) (b) \( f(0) = 3 \) (c) \( f(1) = 3 \)
