Mathematics

Problem

Consider the three real-valued functions given below: a)

f(x)=\dfrac{1}{x^{2}-9}

g(x)=\sqrt{5-2x}

h(x)=\log_{10}(x+4)

Answer the following for each function. a. (i) Write the mathematical condition that must be satisfied by

x

so that

f(x)

is defined. Hence state the domain of

f

. Give a brief reason for your answer. b. (ii) Write the mathematical condition that must be satisfied by

x

so that

g(x)

is defined. Hence state the domain of

g

. Give a brief reason for your answer. c. (iii) Write the mathematical condition that must be satisfied by

x

so that

h(x)

is defined. Hence state the domain of

h

. Give a brief reason for your answer.