Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
Sign in
Please select an account to continue using cracku.in
↓ →
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
$$f$$ and $$g$$ are two real variable real valued functions defined by $$f(x) = x + 2$$ if $$x \ge 0$$, $$f(x) = 2x - 3$$ if $$x < 0$$, and $$g(x) = 3x + 7$$ if $$x \ge 2$$, $$g(x) = x - 1$$ if $$-2 < x < 2$$, $$g(x) = x + 1$$ if $$x \le -2$$. Find $$gof$$.
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is a piecewise function. For $$x \ge 0$$, $$f(x) = x + 2 \ge 2$$, so $$g(f(x)) = 3(x + 2) + 7 = 3x + 13$$. For $$x < 0$$, $$f(x) = 2x - 3 < -3 \le -2$$, so $$g(f(x)) = (2x - 3) + 1 = 2x - 2$$. Hence $$gof(x) = 3x + 13$$ for $$x \ge 0$$ and $$2x - 2$$ for $$x < 0$$.
Was this solution helpful?
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.