Question

Given: g(x)= sqrt x-4 and h(X)=2x-8 . What are the restrictions on the domain of g*h?

Answer 1

6

Explanation:

Answer 2

Given : g(x) =
`√(x-4)` and h(x)=2x-8.

Let us find g*h(x) function now.

g*h(x) = g(x) * h(x) =
`√(x-4)*(2x-8)`

Or g*h(x) =(2x-8)
`√(x-4)`.

He have square root(x-4) in composite function f*h(x).

So, we need to find the domain, we need to check for that values of x's, square root(x-4) would be defined.

Square roots are undefined for negative values.

Therefore, we can setup an inequality for it's domain x-4≥0.

Adding 4 on both sides, we get

x-4+4≥0+4.

x≥4.

Therefore, Domain is all values greater than or equal to 4.

But, restrictions would be all values less than 4 (because less than 4 would give a negative number inside square root).