### Home > APCALC > Chapter 1 > Lesson 1.5.1 > Problem1-196

1-196.

Given the tables below: 1-196 HW eTool (Desmos). Homework Help ✎

 x –2 –1 0 1 2 3 10 100 f(x) –11 –8 –5 –2 1 4 25 295

 x −3 −2 −1 0 1 2 3 12 g(x) −5 0 3 4 3 0 −5 −140

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

2. Evaluate:

1. f(g(h(π)))

2. h(g–1(4))

3. f –1(h(π))

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

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

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

h(π) = −(2)
g(−2) = 0
f(0) = −5
so f(g(h(π))) = −5

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!

Refer to hint in part (ii).

f −1(h(π)) = 1