Mathematics

Mathematics

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)

. a. (i) Find the value of

m

. b. (ii) For this value of

m

, state the domain of

p

. c. (iii) Solve

y=p(x)

for

x

and hence determine the range of

p

. d. (iv) Explain why exactly one real value of

y

is excluded from the range and name that value.

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