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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

π

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.
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