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Let f(x)=x2−4x+3,x<3x−4,x≥3and g(x)=x−3,x<4x2+2x+2,x≥4Then which of the following is/are true?

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a

(f+g)(3.5)=0

b

f(g(3))=3

c

(fg)(2)=1

d

(f−g)(4)=0

answer is A.

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Detailed Solution

(f+g)(3.5)=f(3.5)+g(3.5)=(−0.5)+0.5=0f(g(3))=f(0)=3(fg)(2)=f(2)g(2)=(−1)×(−1)=1(f−g)(4)=f(4)−g(4)=0−26=−26

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Let f(x)=x2−4x+3,x<3x−4,x≥3and g(x)=x−3,x<4x2+2x+2,x≥4Then which of the following is/are true?