Question

Use the functions below for each questions 1 through 4

f(x) = 2x^2 + x -3
h(x)= x-1

1. Determine the domain of f(x) and h(x)
2. Simplify the composition and state its domain. Show work (f ∘ h)(x)
3.Simplify the composition and state its domain. Show work (h∘f)(x)
4. Evalute
(f(h(1))
(h(f(1))

Answer 1

1. For the domain, look for any restrictions where the value of the function would be undefined. If you can’t find any, the domain is all real values.
2. For compositions, you’ll plug one function into the x for another function. The order matters. For (f ∘ h)(x), substitute h = (x-1) for x in f(x). (f ∘ h) = 2(x-1)^2 + (x-1) - 3 = ?
Once you’re done simplifying, determine the domain using the same logic as problem 1.
3. Similar to 2 but this time you’re plugging f into h.
4. Once you have your functions from 2 and 3 you can plug x = 1 into both functions and evaluate.