If f:R to R and g:R to R are given by f(x) = |x| and g(x) = |x| for each x ∈ R , then { x ∈ R:g(

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1.Relation and Function

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If $f:R \to R$ and $g:R \to R$ are given by $f(x) = \;|x|$ and $g(x) = \;|x|$ for each $x \in R$, then $\{ x \in R\;:g(f(x)) \le f(g(x))\} = $

A

$Z \cup ( - \infty ,\;0)$

B

$( - \infty ,0)$

C

$Z$

D

$R$

Solution

(d) $g(f(x)) \le f(g(x))$ ==> $g(|x|) \le f[x]$ ==> $[|x|]\, = \,|[x]|$.

This is true for $x \in R.$.

Standard 12

Mathematics

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