Answer:
g/f = {(-1, 2)}
domain of g/f = {-1}
Step-by-step explanation:
Given,
f = {(-1, 4),(1, 9),(4, 0)},
g = {(-1, -8),(2, -7),(4, 8),(5, -9)}
So, Domain of f = {-1, 1, 4},
Domain of g = {-1, 2, 4, 5}
Since,
[tex]\frac{g}{f}(x) = \frac{g(x)}{f(x)}[/tex]
Thus, domain of g/f = Domain of f ∩ Domain of g = {-1, 4}
If x = -1,
[tex]\frac{g}{f}(-1) = \frac{g(-1)}{f(-1)}=\frac{-8}{-4}=2[/tex]
If x = 4,
[tex]\frac{g}{f}(4) = \frac{g(4)}{f(4)}=\frac{8}{0}=\infty (\text{ not possible})[/tex]
Hence, the domain of g/f = {-1}
And, g/f = {(-1, 2)}
