Question
Show that the function f : N → N defined by f(x) = 2x – 1 is one-one but not onto
✓
Answer
f : N → N
N = {1, 2, 3, 4, 5, …}
f(x) = 2x – 1
f(1) = 2(1) – 1 = 2 – 1 = 1
f(2) = 2(2) – 1 = 4 – 1 = 3
f(3) = 2(3) – 1 = 6 – 1 = 5
f(4) = 2(4) – 1 = 8 – 1 = 7
f(5) = 2(5) – 1 = 10 – 1 = 9
f = {(1, 1) (2, 3) (3, 5) (4, 7) (5, 9) …..}
(i) Different elements have different images. This function is one function.
(ii) Here Range is not equal to co-domain. This function, not an onto function.
∴ The given function is one-one but not an onto.
N = {1, 2, 3, 4, 5, …}
f(x) = 2x – 1
f(1) = 2(1) – 1 = 2 – 1 = 1
f(2) = 2(2) – 1 = 4 – 1 = 3
f(3) = 2(3) – 1 = 6 – 1 = 5
f(4) = 2(4) – 1 = 8 – 1 = 7
f(5) = 2(5) – 1 = 10 – 1 = 9
f = {(1, 1) (2, 3) (3, 5) (4, 7) (5, 9) …..}
(i) Different elements have different images. This function is one function.
(ii) Here Range is not equal to co-domain. This function, not an onto function.
∴ The given function is one-one but not an onto.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove the following identities. $\frac{\cos \theta}{1+\sin \theta}=\sec \theta-\tan \theta$
→Identify rational expression should be subtracted from $\frac{x^2+6 x+8}{x^3+8}$ to get $\frac{3}{x^2-2 x+4}$
→Given that $A=\left[\begin{array}{cc}1 & 3 \\ 5 & -1\end{array}\right], B=\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 5 & 2\end{array}\right], C=\left[\begin{array}{ccc}1 & 3 & 2 \\ -4 & 1 & 3\end{array}\right]$ verify that $A(B+C)=A B+A C$
→Solve the following quadratic equation by formula method
$2 x^2-5 x+2=0$
→$2 x^2-5 x+2=0$
An open box is to be made from a square piece of material, $24$ cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x
→Arul, Madan and Ram working together can clean a store in 6 hours. Working alone, Madan takes twice as long to clean the store as Arul does. Ram needs three times as long as Arul does. How long would it take each if they are working alone?
The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the former number. If the hundreds digit plus twice the tens digit is equal to the units digit, then find the original three-digit number?
A wall clock strikes the bell once at 1 o’clock, 2 times at 2 o’clock, 3 times at 3 o’clock and so on. How many times will it strike in a particular day? Find the standard deviation of the number of strikes the bell make a day.
Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if (A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D) is true?
If $S_n=(x+y)+\left(x^2+x y+y^2\right)+\left(x^3+x^2 y+x y^2+y^3\right)+\ldots n$ terms then prove that $(x-y) S_n=$ $\left[\frac{x^2\left(x^{ n }-1\right)}{x-1}-\frac{y^2\left(y^{ n }-1\right)}{y-1}\right]$
→