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.
State True or False. The function $$f \colon (-\infty, 2] \rightarrow [1, \infty)$$ defined as $$f(x) = x^2 - 4x + 5$$ is a bijection.
Correct Answer: True
$$f(x) = (x - 2)^2 + 1$$. On $$(-\infty, 2]$$ it is strictly decreasing, so it is one-one. Its value is 1 at $$x = 2$$ and increases without bound as $$x \rightarrow -\infty$$, so it takes every value in $$[1, \infty)$$. Hence it is a bijection and the statement is True.
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.