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

Question

Philoid · Accepted Answer

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,