Function Theory

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0 / 6

The graph of y=g(x) is shown in the following for −3≤x≤5.

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Write down the value of g(3)
[1]
Find the value of
1. (g∘g)(5)
  [2]
2. (g−1∘g−1)(1)
  [1]
Sketch the graph of y=g(x+1)−1 on the axes above.
[2]

2

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Consider the functions f(x)=x3−1 and g(x)=2−3x.

Write down the value of g−1(−7).
[1]

Let h(x)=(g∘f)(x)

Find an expression for h(x).
[2]
Find h−1(−19).
[3]

3

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0 / 7

The graph of y=g(x), for −3≤x≤3, is shown in the following diagram.

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Write down the value of
1. g(−2)
  [1]
2. g−1(2)
  [1]
3. g∘g(0)
  [1]
Sketch the graph of y=−g(−x) on the graph above.
[4]

4

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0 / 4

The functions f, g and h are defined by f(x)=1−x, g(x)=3x+2, and h(x)=g∘f(x).

Find an expression for h(x).
[2]
Find h−1(x).
[2]

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7

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9

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