Question

Letf f={(-5,0),(1,9),(4,1)} and g={(-5,-5),(3,0),(4,-2),(5,5)}. Find ( g)/(f) and state its domain.

Answer 1

To find the composition of functions g/f, we need to determine the output of function g when the input is the output of function f.

The composition is {(-5,0), (9,undefined), (1,-2)} and its domain is
`{-5, 1, 4}.`

Step-by-step explanation:

To find the composition of functions
`g/f`, we need to determine the output of function g when the input is the output of function
`f`. Let's start by finding the output of function f for each input:

`f(-5) = 0f(1) = 9f(4) = 1`

Now, we use these outputs as inputs for function g:

`g(0) = -5`

`g(9) =` undefined

`g(1) = -2`

So, the composition of functions g/f is {(-5,0), (9,undefined), (1,-2)}.

The domain of the composition is the set of inputs that produces defined outputs in the composition.

In this case, the domain is
`{-5, 1, 4}.`