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1-196.

Given the tables below, .

 $\boldsymbol{x}$ $\boldsymbol{f(x)}$ $-2$ $−1$ $0$ $1$ $2$ $3$ $10$ $100$ $−11$ $−8$ $−5$ $−2$ $1$ $4$ $25$ $295$

 $\boldsymbol{x}$ $\boldsymbol{g(x)}$ $−3$ $-2$ $−1$ $0$ $1$ $2$ $3$ $12$ $−5$ $0$ $3$ $4$ $3$ $0$ $−5$ $−140$

 $\boldsymbol{x}$ $\boldsymbol{h(x)}$ $−2π$ $−π$ $0$ $\frac { \pi } { 2 }$ $π$ $\frac { 3 \pi } { 2 }$ $2π$ $12π$ $2$ $-2$ $2$ $0$ −2 $0$ $2$ $2$
1. Find possible functions for $f(x)$, $g(x)$, and $h(x)$.

$f(x)$ looks linear.
$g(x)$ looks quadratic.
$h(x)$ looks trigonometric.
Find a transformation that works for each of them.

2. Evaluate:

These composite functions can be evaluated with the table.You do not need to use the equations from part (a).

1. $f(g(h(π)))$

$h(π) = -(2)$
$g(-2) = 0$
$f(0) = -5$
so $f(g(h(π))) = -5$

1. $h(g-1(4))$

$g^{-1}(4)$
Translation: On the $g(x)$ table, what $x$-value has a $y$-value of $4$? Use the table... do NOT find the inverse function... that would be a waste of time!

1. $f -1(h(π))$

Refer to hint in part (ii).

$f^{-1}(h(π)) = 1$

Use the eTool below to explore.
Click the link at right for the full version of the eTool: Calc 1-196 HW eTool