Q.11 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) f is neither one-one nor onto.

Answers (1)

f : R \rightarrow R

f(x) = x^4

One- one:

For   a,b \in R  then f(a) = f(b)

                                  a^{4}=b^{4}

                                  a=\pm b

  \therefore f(a)=f(b) does not imply that a=b

example : f(2)=f(-2)=16    and 2\neq -2 

\therefore  f is not  one- one 

For  2\in R  there is no x in R such that f(x)=x^{4}= 2

\therefore  f is not onto.

Hence, f is neither one-one nor onto. 

Option D is correct.

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