Q3 of 118 Page 3

If f(x) be defined on [–2, 2] and is given by and g(x) = f(|x|) + |f(x)|. Find g(x).

Given and g(x) = f(|x|) + |f(x)|


Now, we have


However, |x| ≥ 0 ⇒ f(|x|) = |x| – 1 when 0 ≤ |x| ≤ 2


We also have



We know



Here, we are interested only in the range [0, 2].



Substituting this value of |x – 1| in |f(x)|, we get




We need to find g(x).


g(x) = f(|x|) + |f(x)|






Thus,


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and

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