Question

Which pairs of function is identical

• A. $f(x)=\sqrt{x^2},g(x)=x$
• B. $f(x)={\sin }^{2}x+{\cos }^{2}x;g(x)=1$
• C. $f(x)=\frac{x}{x},g(x)=1$
• D. None of these

Answer 1

Answer: (B)

For checking equal function
(a) Domain of $f(x)=R$ but range $=[0,\infty )$
Domain of $g(x)=R$, range $=R$
Domain same but range is different so it is not an equal function.
(b) Domain of $f(x)=R$. Domain of $g(x)=R$
Domain and range both same so it is an equal function.
(c) Domain of $f(x)=R-\{0\}.$ Domain of $g(x)=R$
Not equal function as domain is different.