MHT CET · Maths · Functions
If \(f(x)=3[x]+\{x+1\}\), where \([x]\) is greatest integer function of \(x\) and \(\{x\}\) is fractional part function of \(x\), then \(f(-1.32)=\)
- A -4.6
- B -2.6
- C -7.4
- D -3.4
Answer & Solution
Correct Answer
(B) -2.6
Step-by-step Solution
Detailed explanation
\(
\begin{aligned}
& \mathrm{f}(\mathrm{x})=3[\mathrm{x}]+5\{\mathrm{x}+1\} \\
& \mathrm{x}=-1.32 \Rightarrow[\mathrm{x}]=[-1.32]=-2 \\
& \text { Also } \mathrm{x}+1=-1.32+1=-0.32 \\
& \therefore[\mathrm{x}+1]=[-0.32]=-1 \text { and }\{\mathrm{x}+1\}=0.68 \\
& \therefore \mathrm{f}(\mathrm{x})=3(-2)+5(0.68) \\
& =-6+3.4=-2.6
\end{aligned}
\)
\begin{aligned}
& \mathrm{f}(\mathrm{x})=3[\mathrm{x}]+5\{\mathrm{x}+1\} \\
& \mathrm{x}=-1.32 \Rightarrow[\mathrm{x}]=[-1.32]=-2 \\
& \text { Also } \mathrm{x}+1=-1.32+1=-0.32 \\
& \therefore[\mathrm{x}+1]=[-0.32]=-1 \text { and }\{\mathrm{x}+1\}=0.68 \\
& \therefore \mathrm{f}(\mathrm{x})=3(-2)+5(0.68) \\
& =-6+3.4=-2.6
\end{aligned}
\)
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