Q.
Match the entries of Column-I with one or more than one entries of column-II. Note that $[x],\{x\}$ and sgn $x$ denote largest integer less than or equal to $x$, fractional part of $x$ and signum function of $x$ respectively.
Column I
Column II
A
Let $f:[-1,1] \rightarrow R$ be defined by $f(x)=\sqrt[5]{x}+\sin ^{-1} x$ then $f(x)$ is
P
Odd
B
Let $f: R \rightarrow\{-1,0,1\}$ be defined by $f(x)=\operatorname{sgn}\left(\frac{1-|x|}{1+|x|}\right)$ then $f(x)$ is
Q
Even
C
Let $f:[-4,2] \rightarrow[0,3]$ be defined by $f(x)=\sqrt{8-2 x-x^2}$ then $f(x)$ is
R
Onto
D
Let $f :(-\infty, 0] \rightarrow[0, \infty)$ be defined by $f(x)=\frac{2^{-[x]}}{2^{[x]}}-2^{|x|}$ then $f(x)$ is
S
One-One
T
Many-One
| Column I | Column II | ||
|---|---|---|---|
| A | Let $f:[-1,1] \rightarrow R$ be defined by $f(x)=\sqrt[5]{x}+\sin ^{-1} x$ then $f(x)$ is | P | Odd |
| B | Let $f: R \rightarrow\{-1,0,1\}$ be defined by $f(x)=\operatorname{sgn}\left(\frac{1-|x|}{1+|x|}\right)$ then $f(x)$ is | Q | Even |
| C | Let $f:[-4,2] \rightarrow[0,3]$ be defined by $f(x)=\sqrt{8-2 x-x^2}$ then $f(x)$ is | R | Onto |
| D | Let $f :(-\infty, 0] \rightarrow[0, \infty)$ be defined by $f(x)=\frac{2^{-[x]}}{2^{[x]}}-2^{|x|}$ then $f(x)$ is | S | One-One |
| T | Many-One | ||
Inverse Trigonometric Functions
Solution:
