Which of the following pairs of functions are identical?

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Which of the following pairs of functions are identical? (a)

\sqrt{1 + \sin x},\ \sin\frac{x}{2} + \cos\frac{x}{2}

(b)

x,\ \frac{x}{2}

(c)

\sqrt{x^2},\ (\sqrt{x})^2

(d)

\ln x^3 + \ln x^2,\ 5\ln x