Question

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.

Answer 1

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

domain of g/f = {-1}

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,

`(g)/(f)(x) = (g(x))/(f(x))`

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

If x = -1,

`(g)/(f)(-1) = (g(-1))/(f(-1))=(-8)/(-4)=2`

If x = 4,

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

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

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