If f - R- R is defined by fx-x-3-x-4- for x- R - where - - denotes greatest integer function- then limx- 3-fx -

The correct option is C 0 lim h→ 0^+ #160; [ 3 h 3 ]+ | 1 h | = [ h ]+ | 1+h | = 1+1 =0 ...

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Standard XII

Mathematics

Inverse of a Function

If f : R→...

Question

If $f$ : $R \to R$ is defined by $f (x) = [x - 3] + | x - 4 |$ for $x \in R$ , where $[]$ denotes greatest integer function, then $lim x \to 3^{-} f (x) =$

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Solution

The correct option is C $0$
$\begin{matrix} l i m h \to 0^{+} \end{matrix} [3 - h - 3] + | - 1 - h |$
$= [- h] + | 1 + h |$
$= - 1 + 1$
$= 0$

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If f : R→R is defined byf(x)=[x−3]+|x−4| for x∈R , where [] denotes greatest integer function, thenlimx→3−f(x)=

The correct option is C 0limh→0+[3−h−3]+|−1−h|=[−h]+|1+h|=−1+1=0

If $f$ : $R \to R$ is defined by $f (x) = [x - 3] + | x - 4 |$ for $x \in R$ , where $[]$ denotes greatest integer function, then $lim x \to 3^{-} f (x) =$

The correct option is C $0$
$\begin{matrix} l i m h \to 0^{+} \end{matrix} [3 - h - 3] + | - 1 - h |$
$= [- h] + | 1 + h |$
$= - 1 + 1$
$= 0$