Question

show that the function f:N to N defined by f(x)=2x-1 is one-one but not onto

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

It is one-one but not onto.

Step-by-step explanation:

Since we have given that

f: N to N is defined by

$f(x)=2x-1$

For one- one, let x₁, x₂ ε N

So, Let f(x₁) = f(x₂)

$2x_1-1=2x_2-1\\\\2x_1=2x_2\\\\x_1=x_2$

So, it is one-one.

Now, let y = 2x-1

So, we get that

$y+1=2x\\\\\dfrac{y+1}{2}=x$

But if we let y = 2

then, $\dfrac{2+1}{2}=\dfrac{3}{2}=1.5$

And we know that 1.5 does not belong to natural numbers.

Hence, it is one-one but not onto.

# learn more:

F:N to N defined by f(m)=m^2+m+3 is one one function​

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