Functions Ques 6

  1. Let the functions defined in Column I have domain $(-\pi / 2, \pi / 2)$ and range $(-\infty, \infty)$

(1992, 2M)

Column I Column II
A. $1+2 x$ p onto but not one-one
B. $\tan x$ q one-one but not onto
r. one-one and onto
s. neither one-one nor onto
Show Answer

Answer:

Correct Answer: 6.$(A \rightarrow q ; B \rightarrow r)$

Solution: $y=1+2 x$ is linear function, therefore it is one-one and its range is $(-\pi+1, \pi+1)$.

Therefore, $(1+2 x)$ is one-one but not onto so (A) $\rightarrow$ (q). Again, see the figure.

It is clear from the graph that $y=\tan x$ is one-one and onto, therefore $(\mathrm{B}) \rightarrow(\mathrm{r})$.



Table of Contents