Consider the function given by .

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Consider the function

g: \mathbb R \to \mathbb R

given by

g(x)=\log_{2}(x-1)

. (i) Classify

g

according to the list of standard functions. (ii) Find the domain and range of

g

. (iii) Calculate the x-intercept of the graph of

g

. (iv) Show that

g

is a strictly increasing function on its domain. (v) Using the above information, draw a neat sketch of the graph of

g