JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

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Analyzing +4 | -1

f\;:R \to R\;and\,g\;:R \to R

are given by

f\left( x \right) = \left| x \right|\;and\,g\left( x \right) = \left[ x \right]

for each

x \in R,

then

\left\{ {x \in R\;:g\left( {f\left( x \right)} \right) \le f\left( {g\left( x \right)} \right)} \right\} =

View answer and explanation

Correct option: A

Z \cup \left( { - \infty ,0} \right)

Option A (

Z \cup ( - \infty ,0)

) is correct because the inequality holds for all integers and all negative real numbers.

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

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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\}