Question

Which of the following pairs of functions are identical ?

• A. $f\left(x\right)={\log }_{x}e,g\left(x\right)=\frac{1}{{\log }_{e}x}$
• B. $sgn(x^2+1):g\left(x\right)={\sin }^{2}x+{\cos }^{2}x$
• C. $f\left(x\right)={\sec }^{2}x-{\tan }^{2}x;g\left(x\right)={\text{cosec}}^{2}x-{\cot }^{2}x$
• D. $f\left(x\right)=\frac{1}{|x|};g\left(x\right)=\sqrt{x^{-2}}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $f\left(x\right)={\log }_{x}e,g\left(x\right)=\frac{1}{{\log }_{e}x}$
B $sgn(x^2+1):g\left(x\right)={\sin }^{2}x+{\cos }^{2}x$
D $f\left(x\right)=\frac{1}{|x|};g\left(x\right)=\sqrt{x^{-2}}$