lf f:R→R is defined by f(x)=[2x]−2[x] for x∈R where [x] is the greatest integer not exceeding x, then the range of f is

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lf f:R R is defined by f(x)=[2x]-2[x] for x R where [x] is

Question

lf $f : R \to R$ is defined by $f (x) = [2 x] - 2 [x]$
for $x \in R$ where $[x]$ is the greatest integer not exceeding $x$ , then the range of $f$ is

{x \in R : 0 \leq x \leq 1}

{0, 1}

{x \in R : x > 0}

{x \in R : x \geq 0}

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Liam Discussed

f : R \to R

is defined by

f (x) = [2 x] - 2 [x]

for

x \in R

where

[x]

is the greatest integer not exceeding

x

, then the range of

f

12 mins ago

Discuss this question LIVE

12 mins ago

for all

x ϵz; f (x) = 0

If x is not an integer , then

x = [x] + (0, 1)

∴ f (x) [2 [x] + 2 (0, 1)] - 2 [x]

= [2 (0, 1)] = [(0, 2)]

which can take values 0,1

∴

range of f is

{0, 1}

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Question Text	lf $f : R \to R$ is defined by $f (x) = [2 x] - 2 [x]$ for $x \in R$ where $[x]$ is the greatest integer not exceeding $x$ , then the range of $f$ is
Answer Type	Text solution:1
Upvotes	150