Functions Question 430
Question: If f(x) = x and $ g(x)=| x | $ , then $ (f+g)(x) $ is equal to
Options:
A) 0 for all $ x\in R $
B) 2x for all $ x\in R $
C) $ \begin{cases} 2x,forx\ge 0 \\ 0,forx<0 \\ \end{cases} . $
D) $ \begin{cases} 0,forx\ge 0 \\ 2x,forx<0 \\ \end{cases} . $
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Answer:
Correct Answer: C
Solution:
[c] Given functions are: $ f(x)=x $ and $ g(x)=| x | $
$ \therefore (f+g)(x)=f(x)+g(x)=x+| x | $ According to definition of modulus function, $ (f+g)(x)= \begin{cases} x+x,x\ge 0 \\ x-x,x<0 \\ \end{cases} = \begin{cases} 2x,x\ge 0 \\ 0,x<0 \\ \end{cases} . . $
BETA
