FUNCTIONAL NOTATION (problem [1] )
and
COMPOSITE FUNCTIONS (i.e., CHAINS) (problem [2] )
[1] If f(x) = 3x+2 , and if g(x) = x2 - 1, then find the following:
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a] f(1) |
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b] f(0) |
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c] f(-1) |
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d] f(x+1) |
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e] f(x-1) |
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f] f(3x) |
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g] f(3x+2) |
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h] f(-x) |
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i] f(x2) |
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j] f(f(x)) |
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k] f(g(x)) |
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l] g(1) |
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m] g(0) |
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n] g(-1) |
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o] g(x+1) |
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p] g(x-1) |
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q] g(3x) |
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r] g(-x) |
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s] g(x2) |
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t] g(x2-1) |
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u] g(f(x)) |
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v] g(g(x)) |
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| [2]
| The following exercizes practice skills used in THE CHAIN RULE
from Calculus. Composite functions (or chains) have the form y(u(x)). In this situation we may
call u or u(x) the "inner function", and we may call y or y(u)
the "outer function". For the functions h(x) listed below,
choose a u(x) and an y(u), so that their composition
y(u(x)) is equal to the given h(x). |
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Example: If h(x) = (2x + 1)2, choose u = 2x + 1 and y(u) = u2 |
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(3x - 2)
