R D Sharma Solutions for Chapter: Functions, Exercise 6: MULTIPLE CHOICE QUESTIONS (MCQs)

The domain of definition of $f\left(x\right)=\sqrt{x-3-2\sqrt{x-4}}-\sqrt{x-3+2\sqrt{x-4}}$ is

The domain of the function $f\left(x\right)=\sqrt{5\left|x\right|-x^2-6}$ is

The range of the function $f\left(x\right)=\frac{x}{\left|x\right|}$ is

The range of the function $f\left(x\right)=\frac{x+2}{|x+2|}, x\ne -2$ is

The range of the function $f\left(x\right)=|x-1|$ is

Let $f\left(x\right)=\sqrt{x^2+1}.$ Then, which of the following is correct?

If $[x{]}^2-5[x]+6=0,$where [.] denotes the greatest integer function, then

The range of $f\left(x\right)=\frac{1}{1-2\cos x}$ is