### Home > CALC > Chapter 1 > Lesson 1.5.1 > Problem 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*−2

*π*−

*π*0

*π*2

*π*12

*π**h*(*x*)2

−2

2

0

−2

0

2

2

Find possible functions for

*f*(*x*),*g*(*x*), and*h*(*x*).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