Question

Which of the following function is one-one but not onto?

• A. $f : N \rightarrow N , f ( x )=2 x +3$
• B. $f : R \rightarrow R , f ( x )=\frac{4 x +3}{5}$
• C. $f: R \rightarrow R, f(x)=x^3-x$
• D. $f : R \rightarrow R , f ( x )=\ln (| x |+1)$

Answer 1

Answer: (A)

one-one onto means range $\equiv$ Co-domain
(i) $f ( x )=2 x +3$
Range $\in 2 n +3$, where $n \in N$
Range $\neq$ Co-domain
(ii)$f ( x )=\frac{4 x +3}{5} $
$\text { Range }=\text { Co-domain }$
(iii) $f ( x )= x ^3- x$
$\text { Range }=\text { Co-domian }$
(iv) $ f ( x )=\ln (| x |+1)$ even function, many one