Let f (x) be defined on [–π, π] and is given by, f(x)= array ll x & - x 0 x & 0 Let g (x)…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Let f (x) be defined on [–π, π] and is given by,
\(f(x)=\left\{\begin{array}{ll} \sin x & -\pi \leq x \leq 0 \\ \cos x & 0Let g (x) = f |x| + | f (x)|, \(\forall\)x ∈ [–π, π], then
\(f(x)=\left\{\begin{array}{ll} \sin x & -\pi \leq x \leq 0 \\ \cos x & 0
- g (x) = 0, has no real roots
- g (x) = 0, has infinitely many real roots
- g (x) = 0
- limit does not exist at x = 0
Answer
(B) g (x) = 0, has infinitely many real roots, (D) limit does not exist at x = 0
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