The function $ f: R \rightarrow R $ defined by $ f(x)=e^{x} $ is

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

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Understanding +4 | -1

The function

f: R \rightarrow R

defined by

f(x)=e^{x}

View answer and explanation

Correct option: C

One-one and into

Option C (One-one and into) is correct because the exponential function

e^x

is one-to-one over the real numbers and its range is a subset of the codomain R.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

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

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

f: R \rightarrow R

f(x)=x^4

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

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