A function is defined by

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

A function

p

is defined by

p(x)= -\dfrac{m}{x+3}+5

, where

m

is a positive real constant and

x\ne -3

. The graph of

y=p(x)

passes through the point

(1,1)

. (i) Find the value of

m

. (ii) For this value of

m

, state the domain of

p

. (iii) Solve

y=p(x)

for

x

and hence determine the range of

p

. (iv) Explain why exactly one real value of

y

is excluded from the range and name that value.