The function f- N - N defined by fx-2 x-1 is one-to-one-A- TrueB- False

The correct option is A True nbsp;Suppose f(a)=f(b) for a,b∈ N. ⇒ 2a 1=2b 1 ⇒ a=b i.e., nbsp;f(a)=f(b)⇒ a=b ∀ a,b∈ N Thus, the function f is one to one. ...

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Standard X

Mathematics

One to One Function

The function ...

Question

The function $f : N \to N$ defined by $f (x) = 2 x - 1$ is one-to-one.

True

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False

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Solution

The correct option is A True
Suppose $f (a) = f (b)$ for $a, b \in N .$
$\Rightarrow 2 a - 1 = 2 b - 1$
$\Rightarrow a = b$
i.e., $f (a) = f (b) \Rightarrow a = b \forall a, b \in N$
Thus, the function $f$ is one-to-one.

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Similar questions

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The function f:N→N defined by f(x)=2x−1 is one-to-one.

The correct option is A True Suppose f(a)=f(b) for a,b∈N. ⇒2a−1=2b−1 ⇒a=b i.e., f(a)=f(b)⇒a=b ∀a,b∈N Thus, the function f is one-to-one.

The function $f : N \to N$ defined by $f (x) = 2 x - 1$ is one-to-one.

The correct option is A True
Suppose $f (a) = f (b)$ for $a, b \in N .$
$\Rightarrow 2 a - 1 = 2 b - 1$
$\Rightarrow a = b$
i.e., $f (a) = f (b) \Rightarrow a = b \forall a, b \in N$
Thus, the function $f$ is one-to-one.