Question

Let h (x) = 5x − 12 and j (x) = x⁴ + 3 . write the formula defining h ∘ j .

Answer 1

To find the formula defining h ∘ j, substitute h(x) = 5x - 12 into h(x⁴ + 3) to get the final formula: h ∘ j(x) = 5x⁴ + 3.

Step-by-step explanation:

To find the formula defining h ∘ j, we need to compose the functions h(x) and j(x). Composing two functions involves substituting one function into another.

So, h ∘ j(x) = h(j(x)) = h(x⁴ + 3).

Now, we substitute h(x) = 5x - 12 into h ∘ j(x) = h(x⁴ + 3) to get the final formula:

h ∘ j(x) = 5(x⁴ + 3) - 12 = 5x⁴ + 15 - 12 = 5x⁴ + 3.