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Find f ° g and g ° f , where f(x) = 2x 2 and g(x) = x+3, are functions from R to R.

User Yzalavin
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Final answer:

The student needs to find the composite functions f ◦ g and g ◦ f given f(x) = 2x^2 and g(x) = x + 3. To do this, substitute g(x) into f for f ◦ g, and substitute f(x) into g for g ◦ f, then simplify.

Step-by-step explanation:

The student is asking to find the composite functions f ◦ g and g ◦ f, where f(x) = 2x2 and g(x) = x + 3. Composite functions involve applying one function to the result of another function.

To find f ◦ g, we first apply g to x and then apply f to the result of g(x):

f(g(x)) = f(x + 3) = 2(x + 3)2

To find g ◦ f, we first apply f to x and then apply g to the result of f(x):

g(f(x)) = g(2x2) = 2x2 + 3

In each case, we substituted the inside function into the outside function and simplified where possible.

User Lunr
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