Question

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

Answer 1

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