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

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

| –2 | –1 | 0 | 1 | 2 | 3 | 10 | 100 |

| –11 | –8 | –5 | –2 | 1 | 4 | 25 | 295 |

| −3 | −2 | −1 | 0 | 1 | 2 | 3 | 12 |

| −5 | 0 | 3 | 4 | 3 | 0 | −5 | −140 |

| −2 | − | 0 |
| 2 | 12 | ||

| 2 | −2 | 2 | 0 | −2 | 0 | 2 | 2 |

Write possible equations for the functions

*f*,*g*, and*h*.Evaluate:

*f*(*g*(*h*(*π*)))*h*(*g*^{–1}(4))*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. *g*(*x*) looks quadratic. *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