Define and for all with

MATHEMATICS · Multi-part · GCSE · Mathematics · Algebra · Algebra

Problem

Define

f(x)=|x-3|

and

g(x)=x-3

for all

x\in\mathbb R

with

g(x)\neq0

. Consider the quotient function

h(x)=\bigl(\tfrac{f}{g}\bigr)(x)

. Answer the following questions. (i) Express

h(x)

in simplified form for (a)

x>3

and (b)

x<3

, showing each step of your working. (ii) Using your results from part (i), state the complete algebraic description of

h(x)

as a piece-wise defined function. (iii) Determine the domain of

h(x)

, giving reasons for any exclusions. (iv) Evaluate

h(5)

and

h(-2)