How do you find compositions of functions?
Example: (-x Squared)(x-2/5(8))
To find the composition of functions, we need to follow two main steps:
Step 1: Evaluate each function individually, starting from the innermost function and working our way outwards.
In the given example, we have two functions: f(x) = -x^2 and g(x) = (x - 2/5) * 8.
a) Let's evaluate g(x) first:
Replace every occurrence of 'x' in the expression of g(x) with the given input, which is (8):
g(x) = (x - 2/5) * 8
= ((8) - 2/5) * 8
= (8 - 2/5) * 8
= (40/5 - 2/5) * 8
= (38/5) * 8
= 304/5
b) Now, let's evaluate f(x):
Replace every occurrence of 'x' in f(x) with the result we obtained from evaluating g(x), which is (304/5):
f(x) = -x^2
= -(304/5)^2
= -((304/5) * (304/5))
= -(92416/25)
= -3696.64
Therefore, the composition of the functions f(x) and g(x) when evaluated at (x - 2/5(8)) is -3696.64.
Note: In the given example, it seems that there might be a mistake in the parentheses around the term (x - 2/5(8)). If you meant (x - 2/5) * 8, as I assumed, then the above steps are correct.