Question

Which of the following functions (s) has/have the same range?

• A. $f\left(x\right)=\frac{1}{1+x}$
• B. $f\left(x\right)=\frac{1}{1+x^2}$
• C. $f\left(x\right)=\frac{1}{1+\sqrt{x}}$
• D. $f\left(x\right)=\frac{1}{\sqrt{3-x}}$

Answer 1

Answer: (B), (C)

The correct options are
B $f\left(x\right)=\frac{1}{1+x^2}$
C $f\left(x\right)=\frac{1}{1+\sqrt{x}}$

$f\left(x\right)=\frac{1}{1+x}\Rightarrow f\left(x\right)\in (R-\left\{0\right\})f\left(x\right)=\frac{1}{1+x^2}\Rightarrow f\left(x\right)\in (0,1]f\left(x\right)=\frac{1}{1+\sqrt{x}}\Rightarrow f\left(x\right)\in (0,1]f\left(x\right)=\frac{1}{\sqrt{3-x}}\Rightarrow f\left(x\right)\in (0,\infty )$
Hence, options 'B' and 'C' are correct.