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

Question

Which of the following function is one-one but not onto? (A) f: N arrow N , f ( x )=2 x +3 (B) f: R arrow R , f ( x )=(4 x +3/5) (C) f: R arrow R, f(x)=x3-x (D) f: R arrow R , f ( x )= ln (| x |+1)

Tardigrade Admin · Accepted Answer

one-one onto means range ≡ Co-domain (i) f ( x )=2 x +3 Range ∈ 2 n +3, where n ∈ N Range ≠ Co-domain (ii)f ( x )=(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

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

$f : N \to N, f (x) = 2 x + 3$

$f : R \to R, f (x) = \frac{4 x + 3}{5}$

$f : R \to R, f (x) = x^{3} - x$

$f : R \to R, f (x) = ln (∣ x ∣ + 1)$

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) $f (x) = \frac{4 x + 3}{5}$
$Range = Co-domain$
(iii) $f (x) = x^{3} - x$
$Range = Co-domian$
(iv) $f (x) = ln (∣ x ∣ + 1)$ even function, many one

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

f:N→N,f(x)=2x+3

f:R→R,f(x)=54x+3​

f:R→R,f(x)=x3−x

f:R→R,f(x)=ln(∣x∣+1)

one-one onto means range ≡ Co-domain (i) f(x)=2x+3 Range ∈2n+3, where n∈N Range = Co-domain (ii)f(x)=54x+3​ Range = Co-domain (iii) f(x)=x3−x Range = Co-domian (iv) f(x)=ln(∣x∣+1) even function, many one

$f : N \to N, f (x) = 2 x + 3$

$f : R \to R, f (x) = \frac{4 x + 3}{5}$

$f : R \to R, f (x) = x^{3} - x$

$f : R \to R, f (x) = ln (∣ x ∣ + 1)$

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) $f (x) = \frac{4 x + 3}{5}$
$Range = Co-domain$
(iii) $f (x) = x^{3} - x$
$Range = Co-domian$
(iv) $f (x) = ln (∣ x ∣ + 1)$ even function, many one