Search any question & find its solution
Question:
Answered & Verified by Expert
Let $f: R \rightarrow R$ be defined as $f(x)=x^4$. Choose the correct answer.
(a) $f$ is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) fis neither one-one nor onto
(a) $f$ is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) fis neither one-one nor onto
Solution:
2436 Upvotes
Verified Answer
$\mathrm{f}(-1)=(-1)^4=1, \mathrm{f}(1)=1^4=1$
$\therefore-1,1$ have the same image $1 \Rightarrow f$ is not one-one
Further $-2$ in the codomain of $f$ has no pre-image in its domain.
$\therefore \mathrm{f}$ is not onto i.e. f is neither one-one nor onto
Option $(d)$ is correct.
$\therefore-1,1$ have the same image $1 \Rightarrow f$ is not one-one
Further $-2$ in the codomain of $f$ has no pre-image in its domain.
$\therefore \mathrm{f}$ is not onto i.e. f is neither one-one nor onto
Option $(d)$ is correct.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.