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$Given the definitions of f(x) and g(x) below, find the value of f(g(0)). {:[f(x)=3x^(2)+5x+9],[g(x)=3x-1]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(0))$ . $\newline$ $\begin{array}{l} f(x)=3 x^{2}+5 x+9 \\ g(x)=3 x-1 \end{array}$ $\newline$ Answer:

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

f(g(0))

.

\newline

\begin{array}{l} f(x)=3 x^{2}+5 x+9 \\ g(x)=3 x-1 \end{array}

\newline

Answer:

Find $g(0)$ : First, we need to find the value of $g(0)$ by substituting $x = 0$ into the function $g(x)$ . $\newline$ $g(0) = 3(0) - 1$ $\newline$ $g(0) = -1$
Substitute $g(0)$ into $f(x)$ : Now that we have $g(0) = -1$ , we substitute this value into the function $f(x)$ to find $f(g(0))$ . $\newline$ $f(g(0)) = f(-1) = 3(-1)^2 + 5(-1) + 9$
Calculate $f(-1)$ : We perform the calculations within the function $f(x)$ .
$f(-1) = 3(1) + 5(-1) + 9$
$f(-1) = 3 - 5 + 9$
Final value of $f(g(0))$ : We add the numbers to find the final value of $f(g(0))$ . $f(-1) = 3 - 5 + 9$ $f(-1) = -2 + 9$ $f(-1) = 7$

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