Answer:
Step-by-step explanation:
Given:
To find:
the domain of functions f and g
a) To get the domain of f(x), we need to factorise the denominator:
Next, equate the denominator to zero to get the domain:
![\begin{gathered} (x\text{ - 7\rparen}^2\text{ = 0} \\ square\text{ root both sides:} \\ x\text{ - 7 = 0} \\ x\text{ = 7} \\ This\text{ means the value of x cannot be 7 as it will make it undefined} \\ \\ The\text{ domain of f\lparen x\rparen is all real numbers except x = 7} \\ In\text{ interval notation:} \\ (-\infty,\text{ }7)\cup(7,\text{ }\infty) \end{gathered}]()
b) To get the domain of g(x), we will factorise the denominator:
![\begin{gathered} g(x)=\frac{x\text{ - 3}}{x^2-9} \\ x^2\text{ - 9 is a difference of two squares} \\ x^2-3^2\text{ = \lparen x - 3\rparen\lparen x + 3\rparen} \\ \\ equating\text{ the denominator to zero:} \\ (x\text{ - 3\rparen\lparen x + 3\rparen = 0} \\ x\text{ - 3 = 0 or x + 3 = 0} \\ x\text{ = 3 or x = -3} \\ this\text{ means x cannot be equal to -3 or 3 as they will make the function undefined} \\ \\ In\text{ interval notation:} \\ (-\infty,\text{ -3\rparen}\cup(-3,\text{ 3\rparen}\cup(3,\text{ }\infty) \end{gathered}]()