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f(−3.5)=3.75,f(−2)=−3,f(−1)=−5,f(0)=−2f(-3.5) = 3.75, f(-2) = -3, f(-1) = -5, f(0) = -2

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यहाँ दिए गए फलन के लिए f(−3.5)f(-3.5), f(−2)f(-2), f(−1)f(-1), और f(0)f(0) के मान ज्ञात करने हैं:

f(x)={x2+x−5x∈(−∞,0)x2+3x−2x∈[0,∞)f(x) = \begin{cases} x^2 + x - 5 & x \in (-\infty, 0) \\ x^2 + 3x - 2 & x \in [0, \infty) \end{cases}
  1. x=−3.5x = -3.5 के लिए f(x)f(x) का मान ज्ञात करें।

    चूंकि −3.5<0-3.5 < 0 है, हम f(x)=x2+x−5f(x) = x^2 + x - 5 का उपयोग करते हैं।

    f(−3.5)=(−3.5)2+(−3.5)−5f(−3.5)=12.25−3.5−5f(−3.5)=8.75−5f(−3.5)=3.75f(-3.5) = (-3.5)^2 + (-3.5) - 5 \\ f(-3.5) = 12.25 - 3.5 - 5 \\ f(-3.5) = 8.75 - 5 \\ f(-3.5) = 3.75
  2. x=−2x = -2 के लिए f(x)f(x) का मान ज्ञात करें।

    चूंकि −2<0-2 < 0 है, हम f(x)=x2+x−5f(x) = x^2 + x - 5 का उपयोग करते हैं।

    f(−2)=(−2)2+(−2)−5f(−2)=4−2−5f(−2)=2−5f(−2)=−3f(-2) = (-2)^2 + (-2) - 5 \\ f(-2) = 4 - 2 - 5 \\ f(-2) = 2 - 5 \\ f(-2) = -3
  3. x=−1x = -1 के लिए f(x)f(x) का मान ज्ञात करें।

    चूंकि −1<0-1 < 0 है, हम f(x)=x2+x−5f(x) = x^2 + x - 5 का उपयोग करते हैं।

    f(−1)=(−1)2+(−1)−5f(−1)=1−1−5f(−1)=0−5f(−1)=−5f(-1) = (-1)^2 + (-1) - 5 \\ f(-1) = 1 - 1 - 5 \\ f(-1) = 0 - 5 \\ f(-1) = -5
  4. x=0x = 0 के लिए f(x)f(x) का मान ज्ञात करें।

    चूंकि 0≥00 \ge 0 है, हम f(x)=x2+3x−2f(x) = x^2 + 3x - 2 का उपयोग करते हैं।

    f(0)=(0)2+3(0)−2f(0)=0+0−2f(0)=−2f(0) = (0)^2 + 3(0) - 2 \\ f(0) = 0 + 0 - 2 \\ f(0) = -2

    अतः, फलन के मान हैं:
    f(−3.5)=3.75f(-3.5) = 3.75
    f(−2)=−3f(-2) = -3
    f(−1)=−5f(-1) = -5
    f(0)=−2f(0) = -2

    f(−3.5)=3.75,f(−2)=−3,f(−1)=−5,f(0)=−2f(-3.5) = 3.75, f(-2) = -3, f(-1) = -5, f(0) = -2
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