(h o h)(x) if h(x)=x^2 +4
To evaluate the expression (h o h)(x), where h(x) = x^2 + 4, you need to follow these steps:
1. Replace the variable x in h(x) with another variable, let's call it y. So, h(y) = y^2 + 4.
2. Replace the variable y in h(y) with the function h(x). Therefore, h(h(x)) = (h(x))^2 + 4.
3. Replace h(x) in the equation h(h(x)) with its expression x^2 + 4. So, h(h(x)) = (x^2 + 4)^2 + 4.
4. Simplify the expression (x^2 + 4)^2 and add 4. This results in (x^4 + 8x^2 + 16) + 4.
5. Finally, simplify the equation further by combining like terms. The final expression (h o h)(x) = x^4 + 8x^2 + 20.
Therefore, the composition of the function h with itself, (h o h)(x), is x^4 + 8x^2 + 20.