If f:R→R and g:R→R are defined by f(x)=|x| and g(x)=[x−3] for x∈R where ([.] G.I.F) then g(f(x)):−85<x<85=

−85<x<85⇒0≤|x|<85⇒−3<|x|−3<−75[|x|−3]=−3 or −2g(f(x)):−85<x<85=∴{−3,−2}

If f:R→R and g:R→R are defined by f(x)=|x| and g(x)=[x−3] for x∈R where ([.] G.I.F) then g(f(x)):−85<x<85=

−85<x<85⇒0≤|x|<85⇒−3<|x|−3<−75[|x|−3]=−3 or −2g(f(x)):−85<x<85=∴{−3,−2}

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If $f : R \to R$ and $g : R \to R$ are defined by $f (x) = | x |$ and $g (x) = [x - 3]$ for $x \in R$ where $([.] G.I.F)$ then $\{g (f (x)) : \frac{- 8}{5} < x < \frac{8}{5}\} =$

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${- 3, - 2}$

${2, 3}$

${1, 2}$

${0, 1}$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{- 8}{5} < x < \frac{8}{5} \\ \Rightarrow 0 \leq | x | < \frac{8}{5} \Rightarrow - 3 < | x | - 3 < \frac{- 7}{5} \\ [| x | - 3] = - 3 or - 2 \\ \{g (f (x)) : \frac{- 8}{5} < x < \frac{8}{5}\} = ∴ {- 3, - 2} \end{array}$

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If f:R→R and g:R→R are defined by f(x)=|x| and g(x)=[x−3] for x∈R where ([.] G.I.F) then g(f(x)):−85<x<85=

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If $f : R \to R$ and $g : R \to R$ are defined by $f (x) = | x |$ and $g (x) = [x - 3]$ for $x \in R$ where $([.] G.I.F)$ then $\{g (f (x)) : \frac{- 8}{5} < x < \frac{8}{5}\} =$