Question

use the tables on the right to answer #1-2:

1. $(f\circ g)(4) = \underline{quadquad}$ \t 2. $(g\circ f)(5) = \underline{quadquad}$

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$$\begin{tabular}{|c|c|} \\hline x & f(x) \\\\ \\hline 1 & 2 \\\\ \\hline 2 & 1 \\\\ \\hline 3 & 5 \\\\ \\hline 4 & 3 \\\\ \\hline 5 & 4 \\\\ \\hline \\end{tabular}$$

\quad \

$$\begin{tabular}{|c|c|} \\hline x & g(x) \\\\ \\hline 1 & 5 \\\\ \\hline 2 & 4 \\\\ \\hline 3 & 1 \\\\ \\hline 4 & 2 \\\\ \\hline 5 & 3 \\\\ \\hline \\end{tabular}$$

use these functions to answer #3-13. show your work! \t $\

$$\begin{aligned}f(x) &= x - 3 \\\\ g(x) &= x^2 + 9x + 3 \\\\ h(x) &= 2x + 5 \\end{aligned}$$

$
hint: #3-5 should be numerical answers!

1. $f(h(6)) = \underline{quadquad}$ \t 4. $(h\circ g)(3) = \underline{quadquad}$ \t 5. $(g\circ f)(7) = \underline{quadquad}$

Explanation:

Step1: Solve $(f\circ g)(4)$

First find $g(4)$ from the table: $g(4)=2$. Then find $f(2)$ from the table: $f(2)=1$.

Step2: Solve $(g\circ f)(5)$

First find $f(5)$ from the table: $f(5)=4$. Then find $g(4)$ from the table: $g(4)=2$.

Step3: Solve $f(h(6))$

First calculate $h(6)$: $h(6)=2(6)+5=17$. Then calculate $f(17)$: $f(17)=17-3=14$.

Step4: Solve $(h\circ g)(3)$

First calculate $g(3)$: $g(3)=3^2+9(3)+3=9+27+3=39$. Then calculate $h(39)$: $h(39)=2(39)+5=83$.

Step5: Solve $(g\circ f)(7)$

First calculate $f(7)$: $f(7)=7-3=4$. Then calculate $g(4)$: $g(4)=4^2+9(4)+3=16+36+3=55$.

Answer:

1. $(f\circ g)(4)=1$
2. $(g\circ f)(5)=2$
3. $f(h(6))=14$
4. $(h\circ g)(3)=83$
5. $(g\circ f)(7)=55$