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A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 29 Jul 2019, 00:34
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B
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A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4). Which one of the following is negative?

(A) f(0.5)
(B) f(1.5)
(C) f(2.5)
(D) f(3)
(E) f(4.5)
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B
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A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 29 Jul 2019, 00:38
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f(1.5) = .5(-.5)(-1.5)(-2.5) = -ve


IMO B

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A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 29 Jul 2019, 00:43
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Bunuel
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4). Which one of the following is negative?

(A) f(0.5)
(B) f(1.5)
(C) f(2.5)
(D) f(3)
(E) f(4.5)
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f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

(A) f(0.5) ==> -ve*-ve*-ve*-ve ==> +ve
(B)f(1.5) ==> +ve*-ve*-ve*-ve ==> -ve
(C) f(2.5) ==> +ve*+ve*-ve*-ve ==> +ve
(D) f(3) ==> +ve*+ve*0*-ve ==> 0
(E) f(4.5) ==> +ve*+ve*+ve*+ve ==> +ve

Hence B
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A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 29 Jul 2019, 01:16
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f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

X= 1.5
F(x)= +ve*-ve*-ve*-ve= -ve

Answer B

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A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 15 Dec 2021, 11:13
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Given that f(x) = (x – 1)(x – 2)(x – 3)(x – 4) and we need to find which of the answer choice is negative

A. f(0.5)
To find f(0.5) we need to substitute x=0.5 in f(x) = (x – 1)(x – 2)(x – 3)(x – 4)
=> f(0.5) = (0.5 – 1)(0.5 – 2)(0.5 – 3)(0.5 – 4) = NEGATIVE * NEGATIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE

B. f(1.5)
=> f(1.5) = (1.5 – 1)(1.5 – 2)(1.5 – 3)(1.5 – 4) = POSITIVE * NEGATIVE * NEGATIVE * NEGATIVE = NEGATIVE * POSITIVE = NEGATIVE
We don't need to proceed further as we already got the answer. But solving remaining options to complete the solution

C. f(2.5)
=> f(2.5) = (2.5 – 1)(2.5 – 2)(2.5 – 3)(2.5 – 4) = POSITIVE * POSITIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE

D. f(3)
=> f(3) = (3 – 1)(3 – 2)(3 – 3)(3 – 4) = POSITIVE * POSITIVE * ZERO * NEGATIVE = ZERO = NEITHER POSITIVE NOR NEGATIVE

E. f(4.5)
=> f(4.5) = (4.5 – 1)(4.5 – 2)(4.5 – 3)(4.5 – 4) = POSITIVE * POSITIVE * POSITIVE * POSITIVE = POSITIVE * POSITIVE = POSITIVE

So, Answer will be B
Hope it helps!

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