Question

How to find range of a function (without using a graph).Kindly explain with different examples.

Answer 1

The range of a function f(x) is all the possible values which f(x) can take for any x. However, it is necessary, that these values of f(x) must be real and defined. Some of the common rules for f(x) to be real are:
a) If $f\left(x\right)=\frac{1}{a}\to a$ cannot be equal to 0.
b) If $f\left(x\right)=\sqrt{a}\to a$ must be greater than or equal to 0.
c) If $f\left(x\right)=\frac{1}{\sqrt{a}}\to a>0$.
d) If f(x) = log x to base y, then x >0, y > 0 and y cannot be equal to 1.
Similarly you can find different situations and make rules such that f(x) is real and defined.