JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

f:R \to R

is defined by

f\left( x \right) = \frac{{{e^{{x^2}}} - {e^{ - {x^2}}}}}{{{e^{{x^2}}} + {e^{ - {x^2}}}}},

View answer and explanation

Correct option: A

One-one but not onto

Option D is correct. The function is neither one-one nor onto because

f(-x) = f(x)

, making it many-to-one, and the range is a subset of R, not all of R, making it 'into'.

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f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

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