Previous Year NEET Question- Relations & Functions

• 2019: The range of the function $f(x) = \frac{x^2 + 1}{x^2 - 1}$ is all real numbers except $\frac{1}{2}$.

To find the range of a function, we need to find all the values that the function can output. In this case, the function can output any real number except 1. This is because the function is undefined at $x = \pm 1$, and any value of $x$ that is not equal to $\pm 1$ will result in a real number output.

The reason why the function is undefined at $x = \pm 1$ is because the denominator of the function is equal to 0 at those values. When the denominator of a fraction is equal to 0, the fraction is undefined.

Therefore, the range of the function $f(x) = \frac{x^2 + 1}{x^2 - 1}$ is all real numbers except $\frac{1}{2}$.

• 2018: Let $f(x) = \frac{x^2 + x + 1}{x^2 + 2x + 1}$. Then $