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

Understand Composition of Functions: Understand the composition of functions. The composition of two functions f and g, denoted as (f@g)(x), means that we first apply g to x, and then apply f to the result of g(x). So, (f@g)(x) = f(g(x)).Find g(0): Find g(0). We are given g(x) = 4x. To find g(0), we substitute x with 0. g(0) = 4 * 0 = 0.Find f(g(0): Find f(g(0)). Now that we know g(0) = 0, we need to find f(0). We are given f(x) = x + 6. So, we substitute x with 0. f(0) = 0 + 6 = 6.Find (f@g)(0): Find (f@g)(0). Since we have found that g(0) = 0 and f(0) = 6, we can now find (f@g)(0) which is f(g(0)). (f@g)(0) = f(0) = 6.

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Find $(f \circ g)(0)$ . $f(x) = x + 6$ , $g(x) = 4x$

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Q. Find

(f \circ g)(0)

f(x) = x + 6

g(x) = 4x

Understand Composition of Functions: Understand the composition of functions. The composition of two functions $f$ and $g$ , denoted as $(f@g)(x)$ , means that we first apply $g$ to $x$ , and then apply $f$ to the result of $g(x)$ . So, $(f@g)(x) = f(g(x))$ .
Find $g(0)$ : Find $g(0)$ . We are given $g(x) = 4x$ . To find $g(0)$ , we substitute $x$ with $0$ . $g(0) = 4 \times 0 = 0$ .
Find $f(g(0))$ : Find $f(g(0))$ . Now that we know $g(0) = 0$ , we need to find $f(0)$ . We are given $f(x) = x + 6$ . So, we substitute $x$ with $0$ . $f(0) = 0 + 6 = 6$ .
Find $(f@g)(0)$ : Find $(f@g)(0)$ . $\newline$ Since we have found that $g(0) = 0$ and $f(0) = 6$ , we can now find $(f@g)(0)$ which is $f(g(0))$ . $\newline$ $(f@g)(0) = f(0) = 6$ .