Find (f@g)(0). {:[f(x)=x+5],[g(x)=x^(2)+3],[(f@g)(0)=]:}

Understand Function Composition: Understand the composition of functions. The composition of two functions (f@g)(x) means that we first apply g to x, and then apply f to the result of g(x). In mathematical terms, (f@g)(x) = f(g(x)).Calculate g(0): Calculate g(0). We need to find the value of g(x) when x = 0. Since g(x) = x^2 + 3, we substitute x with 0. g(0) = (0)^2 + 3 = 0 + 3 = 3.Calculate f(g(0): Calculate f(g(0)). Now that we have g(0) = 3, we need to find f(g(0)) which is f(3). Since f(x) = x + 5, we substitute x with 3. f(3) = 3 + 5 = 8.Conclude (f@g)(0): Conclude the value of (f@g)(0). We have found that f(g(0)) = f(3) = 8. Therefore, (f@g)(0) = 8.

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Find derivatives of sine and cosine functions

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Q. Find

(f \circ g)(0)

\newline

\begin{align*} &f(x) = x + 5,\ &g(x) = x^{2} + 3,\ &(f \circ g)(0) = \end{align*}

Understand Function Composition: Understand the composition of functions. The composition of two functions $(f \circ g)(x)$ means that we first apply $g$ to $x$ , and then apply $f$ to the result of $g(x)$ . In mathematical terms, $(f \circ g)(x) = f(g(x))$ .
Calculate $g(0)$ : Calculate $g(0)$ . $\newline$ We need to find the value of $g(x)$ when $x = 0$ . Since $g(x) = x^2 + 3$ , we substitute $x$ with $0$ . $\newline$ $g(0) = (0)^2 + 3 = 0 + 3 = 3$ .
Calculate $f(g(0))$ : Calculate $f(g(0))$ . Now that we have $g(0) = 3$ , we need to find $f(g(0))$ which is $f(3)$ . Since $f(x) = x + 5$ , we substitute $x$ with $3$ . $f(3) = 3 + 5 = 8$ .
Conclude $(f@g)(0)$ : Conclude the value of $(f@g)(0)$ . We have found that $f(g(0)) = f(3) = 8$ . Therefore, $(f@g)(0) = 8$ .