Question

Let f(x) = Square root of 6x and g(x) = x - 3. What's

the smallest number that is in the domain of
fºg?

Answer 1

Answer: on Plato I got it wrong for the answer 3

Explanation:

Answer 2

For this case we have the following equations:

`f (x) = \sqrt {6x}\\g (x) = x-3`

We must find
`(f_ {o} g) (x):`

By definition of composition of functions we have to:

`(f_ {o} g) (x) = f (g (x))`

So:

`(f_ {o} g) (x) = \sqrt {6 (x-3)}`

We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined. That is to say:

`6 (x-3) \geq0\\(x-3) \geq0\\x \geq3`

Then, the domain is given by [3, ∞)

Answer:

The smallest number that is the domain of the composite function is 3