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.