Answer the following questions related to the idea of the domain of a real-valued…

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Answer the following questions related to the idea of the domain of a real-valued function. (i) Define the domain of a real-valued function. (ii) For

g(x)=\sqrt{3x-2}

, write the algebraic condition that

x

must satisfy and briefly explain why this condition is necessary. (iii) For

h(x)=\dfrac{1}{x^{2}-4}

, state the values of

x

that are excluded from the domain and give a reason for each exclusion. (iv) For

p(x)=\log_{2}(x+7)

, state the condition on

x

that ensures

p(x)

is defined and explain your reasoning.