Question

Assertion :Let $f:[0,2]\to [0,2]$ be a continuous function.

$f\left(x\right)=x$ for at least one $0\le x\le 2$

Reason: $f\left(x\right)=-x$ for at least one $0\le x\le 2$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

the range of f is $[0,2]$ and the domain is $[0,2]$

given that $f\left(x\right)$ is continuous.

so it must cross $y=x$ line atleast once because it cant cover every point in the range without crossing $y=x$ line.

but it doesn't cross $y=-x$ because the function is in first quadrant and $f\left(x\right)=-x$ lies on second quadrant.

so assertion is correct but reason is wrong.