Answer :
Answer:
1) x≠7
2) x≠3 or -7
Step-by-step explanation:
1. The given function is
[tex]f(x) = \frac{1}{x - 7} [/tex]
This function is undefined if the denominator is equal to zero .
Therefore the restriction is that:
The denominator is not zero.
[tex]x - 7 \ne0[/tex]
[tex]x \ne7[/tex]
2) Assuming the second function is
[tex]f(x) = \frac{(x + 7)(x - 9)}{(x - 3)(x + 7)} [/tex]
This function is not defined when the denominator is zero.
This implies that:
[tex](x - 3)(x + 7) \ne0[/tex]
The restrictions are:
[tex]x \ne3 \: or \: - 7[/tex]