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ira [324]
3 years ago
9

Let f=​{(-1, 4)​,(1, 9)​,(4, 0)​} and g=​{(-1, -8)​,(2, -7)​,(4, 8)​,(5, -9)​}. Find​ g/f and state its domain.

Mathematics
1 answer:
tekilochka [14]3 years ago
4 0

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,

\frac{g}{f}(x) = \frac{g(x)}{f(x)}

Thus, domain of g/f = Domain of f ∩ Domain of g = {-1, 4}

If x = -1,

\frac{g}{f}(-1) = \frac{g(-1)}{f(-1)}=\frac{-8}{-4}=2

If x = 4,

\frac{g}{f}(4) = \frac{g(4)}{f(4)}=\frac{8}{0}=\infty (\text{ not possible})

Hence, the domain of g/f = {-1}

And, g/f = {(-1, 2)}

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