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$Review of 5.3, 5.4, and 5.5 Perform the indicated operation. 1) {:[g(a)=2a-4],[h(a)=-4a-2quad6a-2],[" Find "(g-h)(a)]:} {:[g(n)=2n-3],[f(n)=2n^(2)+5n],[" Find "g(n)+f(n)]:} {:[f(a)=-a^(3)-3a],[g(a)=-4a+2],[" Find "f(-3)+g(-3)]:} {:[g(x)=-x-3],[f(x)=x^(2)-5x],[" Find "g(x)*f(x)]:} {:[f(n)=n+2],[g(n)=4n+4],[" Find "f(-3)*g(-3)]:}$

Review of $5$ . $3$ , $5$ . $4$ , and $5$ . $5$ $\newline$ Perform the indicated operation. $\newline$ $1$ ) $\newline$ $\begin{array}{l} g(a)=2 a-4 \\ h(a)=-4 a-2 \quad 6 a-2 \\ \text { Find }(g-h)(a) \end{array}$ $\newline$ $3$ ) $\newline$ $\begin{array}{l} g(n)=2 n-3 \\ f(n)=2 n^{2}+5 n \\ \text { Find } g(n)+f(n) \end{array}$ $\newline$ $5$ ) $\newline$ $\begin{array}{l} f(a)=-a^{3}-3 a \\ g(a)=-4 a+2 \\ \text { Find } f(-3)+g(-3) \end{array}$ $\newline$ $7$ ) $\newline$ $\begin{array}{l} g(x)=-x-3 \\ f(x)=x^{2}-5 x \\ \text { Find } g(x) \cdot f(x) \end{array}$ $\newline$ $9$ ) $\newline$ $\begin{array}{l} f(n)=n+2 \\ g(n)=4 n+4 \\ \text { Find } f(-3) \cdot g(-3) \end{array}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Review of

5

3

5

4

, and

5

5

\newline

Perform the indicated operation.

\newline

1

)

\newline

\begin{array}{l} g(a)=2 a-4 \\ h(a)=-4 a-2 \quad 6 a-2 \\ \text { Find }(g-h)(a) \end{array}

\newline

3

)

\newline

\begin{array}{l} g(n)=2 n-3 \\ f(n)=2 n^{2}+5 n \\ \text { Find } g(n)+f(n) \end{array}

\newline

5

)

\newline

\begin{array}{l} f(a)=-a^{3}-3 a \\ g(a)=-4 a+2 \\ \text { Find } f(-3)+g(-3) \end{array}

\newline

7

)

\newline

\begin{array}{l} g(x)=-x-3 \\ f(x)=x^{2}-5 x \\ \text { Find } g(x) \cdot f(x) \end{array}

\newline

9

)

\newline

\begin{array}{l} f(n)=n+2 \\ g(n)=4 n+4 \\ \text { Find } f(-3) \cdot g(-3) \end{array}

Subtract and Simplify: $g(a) = 2a - 4$ , $h(a) = -4a - 2$ . To find $(g - h)(a)$ , subtract $h(a)$ from $g(a)$ . $(g - h)(a) = (2a - 4) - (-4a - 2)$ $(g - h)(a) = 2a - 4 + 4a + 2$ $(g - h)(a) = 6a - 2$
Add and Simplify: $g(n) = 2n - 3$ , $f(n) = 2n^2 + 5n$ . To find $g(n) + f(n)$ , add $f(n)$ to $g(n)$ . $\newline$ $g(n) + f(n) = (2n - 3) + (2n^2 + 5n)$ $\newline$ $g(n) + f(n) = 2n^2 + 7n - 3$
Substitute and Add: $f(a) = -a^3 - 3a$ , $g(a) = -4a + 2$ . To find $f(-3) + g(-3)$ , substitute $-3$ into both $f(a)$ and $g(a)$ and add the results. $\newline$ $f(-3) = -(-3)^3 - 3(-3)$ $\newline$ $f(-3) = -(-27) + 9$ $\newline$ $f(-3) = 27 + 9$ $\newline$ $f(-3) = 36$ $\newline$ $g(a) = -4a + 2$ $0$ $\newline$ $g(a) = -4a + 2$ $1$ $\newline$ $g(a) = -4a + 2$ $2$ $\newline$ $g(a) = -4a + 2$ $3$ $\newline$ $g(a) = -4a + 2$ $4$
Multiply and Simplify: $g(x) = -x - 3$ , $f(x) = x^2 - 5x$ . To find $g(x) \times f(x)$ , multiply $g(x)$ by $f(x)$ .
$g(x) \times f(x) = (-x - 3) \times (x^2 - 5x)$
$g(x) \times f(x) = -x^3 + 5x^2 + 3x^2 - 15x$
$g(x) \times f(x) = -x^3 + 8x^2 - 15x$
Substitute and Multiply: $f(n) = n + 2$ , $g(n) = 4n + 4$ . To find $f(-3) \times g(-3)$ , substitute $-3$ into both $f(n)$ and $g(n)$ and multiply the results. $\newline$ $f(-3) = -3 + 2$ $\newline$ $f(-3) = -1$ $\newline$ $g(-3) = 4(-3) + 4$ $\newline$ $g(-3) = -12 + 4$ $\newline$ $g(n) = 4n + 4$ $0$ $\newline$ $g(n) = 4n + 4$ $1$ $\newline$ $g(n) = 4n + 4$ $2$