f(x)=x g(x)=-x find [f o g ](2) [g o f] (2)

Understand Function Composition: Understand the composition of functions. The composition of two functions [f o g](x) means we first apply g to x, and then apply f to the result of g(x). Similarly, [g o f](x) means we first apply f to x, and then apply g to the result of f(x).Calculate [f o g](2): Calculate [f o g](2). First, we find g(2) which is -2 since g(x) = -x. Then we apply f to this result, so f(g(2)) = f(-2) = -2, because f(x) = x.Calculate [g o f](2): Calculate [g o f](2). First, we find f(2) which is 2 since f(x) = x. Then we apply g to this result, so g(f(2)) = g(2) = -2, because g(x) = -x.Verify Results: Verify the results and answer the question prompt. We have found that [f o g](2) = -2 and [g o f](2) = -2. Both compositions yield the same result when evaluated at x = 2.

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Math Problems

Calculus

Find derivatives of sine and cosine functions

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f(x)=x

g(x)=-x

find

[f \circ g ](2)

[g \circ f] (2)

Understand Function Composition: Understand the composition of functions. The composition of two functions $[f \circ g](x)$ means we first apply $g$ to $x$ , and then apply $f$ to the result of $g(x)$ . Similarly, $[g \circ f](x)$ means we first apply $f$ to $x$ , and then apply $g$ to the result of $f(x)$ .
Calculate $[f \circ g](2)$ : Calculate $[f \circ g](2)$ . $\newline$ First, we find $g(2)$ which is $-2$ since $g(x) = -x$ . Then we apply $f$ to this result, so $f(g(2)) = f(-2) = -2$ , because $f(x) = x$ .
Calculate $[g \circ f](2)$ : Calculate $[g \circ f](2)$ . First, we find $f(2)$ which is $2$ since $f(x) = x$ . Then we apply $g$ to this result, so $g(f(2)) = g(2) = -2$ , because $g(x) = -x$ .
Verify Results: Verify the results and answer the question prompt. $\newline$ We have found that $[f \circ g](2) = -2$ and $[g \circ f](2) = -2$ . Both compositions yield the same result when evaluated at $x = 2$ .