JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

Let

f: \mathbb{R} \rightarrow \mathbb{R}

be a function such that

f(x)=\frac{x^{2}+2 x+1}{x^{2}+1}

. Then

View answer and explanation

Correct option: B

f(x)

is one-one in

[1, \infty)

but not in

(-\infty, \infty)

Option B (

f(x)

is one-one in

[1, \infty)

but not in

(\infty, \infty)

) is correct because the function is one-to-one in the specified interval, but not over the entire real number line.

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f\left( x \right) = x - \left[ x \right]

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f(x)=x^4

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S=\left\{x: f(x)=f^{-1}(x)\right\}