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Home > CALC > Chapter 1 > Lesson 1.5.1 > Problem 1-196

1-196.
  1. 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. Find possible functions for f(x), g(x), and h(x).

    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