{:[" Find "(f@g)(0)". "],[f(x)=6x],[g(x)=x^(2)+4x]:}

Understand Composition of Functions: First, we need to understand what the composition of functions (f@g)(x) means. It means that we first apply the function g to x, and then apply the function f to the result of g(x). So, (f@g)(x) = f(g(x)).Find g(0): Given the functions f(x) = 6x and g(x) = x^2 + 4x, we need to find g(0) first, since we are looking for (f@g)(0).Calculate g(0): To find g(0), we substitute x with 0 in the function g(x): g(0) = 0^2 + 4*0.Find f(g(0)): Calculating g(0) gives us g(0) = 0 + 0, which simplifies to g(0) = 0.Calculate f(0): Now that we have g(0), we need to find f(g(0)). Since g(0) = 0, we need to find f(0).Final Result: To find f(0), we substitute x with 0 in the function f(x): f(0) = 6*0.Calculating f(0) gives us f(0) = 0, which means that (f@g)(0) = f(g(0)) = f(0) = 0.

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Find derivatives of logarithmic functions

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Q. Find

(f \circ g)(0)

f(x) = 6x

g(x) = x^{2} + 4x

Understand Composition of Functions: First, we need to understand what the composition of functions $(f@g)(x)$ means. It means that we first apply the function $g$ to $x$ , and then apply the function $f$ to the result of $g(x)$ . So, $(f@g)(x) = f(g(x))$ .
Find $g(0)$ : Given the functions $f(x) = 6x$ and $g(x) = x^2 + 4x$ , we need to find $g(0)$ first, since we are looking for $(f@g)(0)$ .
Calculate $g(0)$ : To find $g(0)$ , we substitute $x$ with $0$ in the function $g(x)$ : $g(0) = 0^2 + 4\cdot0$ .
Find $f(g(0))$ : Calculating $g(0)$ gives us $g(0) = 0 + 0$ , which simplifies to $g(0) = 0$ .
Calculate $f(0)$ : Now that we have $g(0)$ , we need to find $f(g(0))$ . Since $g(0) = 0$ , we need to find $f(0)$ .
Final Result: To find $f(0)$ , we substitute $x$ with $0$ in the function $f(x)$ : $f(0) = 6 \times 0$ .
Final Result: To find $f(0)$ , we substitute $x$ with $0$ in the function $f(x)$ : $f(0) = 6\times0$ .Calculating $f(0)$ gives us $f(0) = 0$ , which means that $(f@g)(0) = f(g(0)) = f(0) = 0$ .