$f(x)=\sqrt{1+x+x^2}-\sqrt{1-x+x^2}$ is

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

$f(x)=\sqrt{1+x+x^2}-\sqrt{1-x+x^2}$ is :

Options:

even

odd

neither even nor odd

None of these

Correct Answer:

odd

Explanation:

$f(-x)= \sqrt{1+(-x)+(-x)^2}-\sqrt{1-(-x)+(-x)^2}$

$\sqrt{1-x+x^2}-\sqrt{1+x+x^2}$ = – f(x). Hence f(x) is odd.

Hence (2) is the correct answer.