when is (f of h)(x) if f(x)=2x^2-5 and h(x)=sqrt x-3 then simplify answer and give the domain in interval notation
To find (f∘h)(x), we first need to substitute h(x) into f(x):
f(h(x)) = 2(sqrt(x)-3)^2 - 5
= 2(x-6sqrt(x)+9) - 5
= 2x - 12sqrt(x) + 18 - 5
= 2x - 12sqrt(x) + 13
Therefore, (f∘h)(x) = 2x - 12√x + 13.
The domain of the function (f∘h)(x) is restricted by the square root function in h(x), so x must be greater than or equal to 3 for the function to be defined.
Therefore, the domain of (f∘h)(x) in interval notation is [3, ∞).