If f : R → R and g : R → R are given by f(x) = |x| and g(x) = [x], then g ( f ( x ) ) ≤ f ( g ( x ) is true for - Options: A . &nbsp Z ∪ ( − ∞ , 0 ) B . &nbsp ( − ∞ , 0 ) C . &nbsp Z D . &nbsp R

Answer: Option D : D g ( f ( x ) ) ≤ f ( g ( x ) ) ⇒ g ( | x | ) ≤ f [ x ] ⇒ [ | x | ] ≤ | [ x ] | This is true for x ϵ R . .

If f:R→R and g:R→R are given by f(x) = |x| and g(x) = [x], then

Question -

If $f : R \to R$ and $g : R \to R$ are given by f(x) = |x| and g(x) = [x], then $g (f (x)) \leq f (g (x)$ is true for -

Options:

A .

Z \cup (- \infty, 0)

B .

(- \infty, 0)

C .

Z

D .

R

Answer: Option D
:
D

g (f (x)) \leq f (g (x)) \Rightarrow g (| x |) \leq f [x] \Rightarrow [| x |] \leq | [x] |

This is true for

x ϵ R .

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