Algebra

Relations & Functions

Medium

core

Let N be the set of natural numbers and R be the set of all real numbers. If function $f:N\to R$ defined by $f(x)=4x^2+12x+15$ , then $f:N\to range(f)$ is

One-one but not onto

Onto but not one-one

One-one and onto

Neither one-one nor onto

✅ Correct Option: 3

$f(x)=(2x+3)^2+6$ is strictly increasing for $x\ge1$ , so distinct naturals give distinct images and $f$ is one-one.

Restricting the codomain to the range makes every image attained, so it is also onto, hence bijective.

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Which of the following graphs represent a function ?

Let N be the set of natural numbers and R be the set of all real numbers. If function f:N→Rf:N\to Rf:N→R defined by f(x)=4x2+12x+15f(x)=4x^2+12x+15f(x)=4x2+12x+15, then f:N→range(f)f:N\to range(f)f:N→range(f) is