Functions Ques 6
- Let the functions defined in Column I have domain $(-\pi / 2, \pi / 2)$ and range $(-\infty, \infty)$
(1992, 2M)
| Column I | Column II | ||
|---|---|---|---|
| A. | $1+2x$ | p | onto but not one-one |
| B. | $\tan x$ | q | one-one but not onto |
| r. | one-to-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 $(-\infty, \infty)$.
Therefore, $(1+2x)$ 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 not one-one and onto, therefore $(\mathrm{B}) \rightarrow(\mathrm{r})$.
BETA
