Question

Consider the following statements:
(1) If $f\left(x\right)=x^3$ and $g\left(y\right)=y^3$ then $f=g$.
(2) Identity function is not always a bijection.
Which of the above statements is/are correct?

• A. (1) only
• B. (2) only
• C. Both (1) and (2)
• D. Neither (1) and (2)

Answer 1

The correct option is D Neither (1) and (2)

For two function to be equal its domain and range must be equal.Here, domain and range is not clear as the set over which the function is defined is not given.

So, we can't conclude $f=g$
And identity function is always bijection.
Option D is correct.