JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

Which of the following functions is (are) not an injective map(s)?

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Correct option: B

\mathrm{g}\left( x \right) = x + \frac{1}{x},x \in \left( {0,\infty } \right)

The correct answer is

\mathrm{g}\left( x \right) = x + \frac{{1}}{{x}},x \in \left( {0,\infty } \right)

because it is not injective; g(2) = g(1/2) = 5/2, demonstrating that different inputs can yield the same output.

More Questions from FUNCTIONS

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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\}