CPM Homework Help : CALC Problem 1-196

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1-196.

Given the tables below, .

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

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

$\boldsymbol{x}$	$−2π$	$−π$	$0$	$\frac { \pi } { 2 }$	$π$	$\frac { 3 \pi } { 2 }$	$2π$	$12π$
$\boldsymbol{h(x)}$	$2$	$-2$	$2$	$0$	−2	$0$	$2$	$2$

Find possible functions for $f(x)$ , $g(x)$ , and $h(x)$ .
Hint (a):
$f(x)$ looks linear.
$g(x)$ looks quadratic.
$h(x)$ looks trigonometric.
Find a transformation that works for each of them.
Evaluate:
Hint (b):
These composite functions can be evaluated with the table.You do not need to use the equations from part (a).
1. $f(g(h(π)))$
  Answer (i):
  $h(π) = -(2)$
  $g(-2) = 0$
  $f(0) = -5$
  so $f(g(h(π))) = -5$
1. $h(g-1(4))$
  Hint (ii):
  $g^{-1}(4)$
  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. $f -1(h(π))$
  HInt (iii):
  Refer to hint in part (ii).
  Answer (iii):
  $f^{-1}(h(π)) = 1$

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