Question
Question: If f(x) = sin(cosx) − x + tan(sinx) ∀ x ∈ (-∞, 0) then odd extension of f(x) in (0, ∞) is...
If f(x) = sin(cosx) − x + tan(sinx) ∀ x ∈ (-∞, 0) then odd extension of f(x) in (0, ∞) is
A
sin(cos x) + x + tan (sinx)
B
sin (cosx) + x − tan (sinx)
C
sin (cosx) − x + tan (sinx)
D
−x − sin (cosx) + tan (sinx)
Answer
−x − sin (cosx) + tan (sinx)
Explanation
Solution
Odd extension of f(x) in (0, ∞) can be obtained by replacing x by -x and multiplying throughout by -ve sign.