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प्रश्न
A function f: [– 5, 9] → R is defined as follow :
f(x) = `{{:(6x + 1";", -5 ≤ x < 2),(5x^2 - 1";", 2 ≤ x < 6),(3x - 4";", 6 ≤ x ≤ 9):}` Find `(2"f"(- 2) - "f"(6))/("f"(4) + "f"( -2))`
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उत्तर
f(x) = 6x + 1; x = {– 5, – 4, – 3, – 2, – 1, 0, 1}
f(x) = 5x2 – 1; x = {2, 3, 4, 5}
f(x) = 3x – 4; x = {6, 7, 8, 9}
`(2"f"(- 2) - "f"(6))/("f"(4) + "f"( -2))`
f(x) = 6x + 1
f(– 2) = 6(– 2) + 1 = – 12 + 1 = – 11
f(x) = 3x – 4
f(6) = 3(6) – 4 = 18 – 4 = 14
f(x) = 5x2 – 1
f(4) = 5(4)2 – 1 = 5(16) – 1
= 80 – 1 = 79
f(x) = 6x + 1
f(– 2) = 6(– 2) + 1 = – 12 + 1 = – 11
`(2"f"(- 2) - "f"(6))/("f"(4) + "f"( -2)) = (2(- 11) - 14)/(79 - 11)`
= `(- 22 - 14)/(68)`
= `(-36)/(68)`
= `(-9)/(17)`
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