Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f g(x), then which of the following statements is/are correct ? I. q(x) is continuous at x=0. II. q(x) is differentiable at x=0. Select the answer using the code given below :

Question

Quantrex Academy · Accepted Answer

Correct answer: C. Both I and II

Given f(x) = (x^2) and g(x) = x|x|. The composite function q(x) is given by: q(x) = f(g(x)) = f(x|x|) = ((x|x|)^2) Since (x|x|)^2 = x^2|x|^2 = x^4, we have: q(x) = (x^4) Checking continuity at x=0: _ x 0 q(x) = _ x 0 (x^4) = 0 Also, q(0) = (0) = 0. Since _ x 0 q(x) = q(0), q(x) is continuous at x=0. Statement I is correct. Checking differentiability at x=0: q'(0) = _ x 0 q(x) - q(0) x - 0 = _ x 0 (x^4) x q'(0) = _ x 0 ( (x^4) x^4 x^3 ) = 1 0 = 0 Since the limit exists and is finite, q(x) is differentiable at x=0. Statement II is correct. Both statements I and II are correct. Answer: Both I and II

NDA Mathematics Question (2026) — Solution

Question

Options

Answer

Step-by-step solution