Question

Assertion (A) : $f\left(x\right)=\frac{x^2-4}{x-2}$ and $g\left(x\right)=x+2$ are equal.
Reason (R): Two functions $f$ and $g$ are said to be equal if their domains and ranges are equal and $f\left(x\right)=g\left(x\right)\forall x\in$ domain.

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
• B. Both $A$ and $R$ are true and $R$ is not correct explanation of $A$
• C. $A$ is true but $R$ is false
• D. $A$ is false but $R$ is true

Answer 1

The correct option is D $A$ is false but $R$ is true

The domain for $f\left(x\right)$ is $R-\left\{2\right\}$ and domain of $g\left(x\right)$ is $R$. Hence Assertion is false as the domain is not equal.

Reason is true as two functions $f$ and $g$ are said to be equal if

The domain of $f$ = domain of $g$.

The co-domain of $f$ = co-domain of $g$.

The range of $f$ = range of $g$.