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Composite functions
1.
Block 3 Composite Functions
2.
What is to
be Learned • What a composite function is • How to express a composite function
3.
Definition • A number
(or letter) is affected by more than one function
4.
f(x) = 3x
and g(x) = x2 Combining these: Multiply by 3, then square or Square, then multiply by 3 Not the same! Multiply by 3 Square
5.
f(x) = x2 f(4)
= 16 f(16) = 162 f( ) ?f(4) f( )f(4)16
6.
f(x) = 3x
+ 2 f(4) = 14 f(14) = 3(14) + 2 f( ) ?f(4) f( )f(4)14
7.
Combination of more
than one function. If f(x) = 4x and g(x) = x2 g( f(3) )? f(3) = 12 so g( f(3) ) = g (12 ) = = 144 122 Composite Functions
8.
With Formulas f(x)= 2x
+ 1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) g(f(x)) Change this
9.
f(x)= 2x +
1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) Change this g(f(x))
10.
f(x)= 2x +
1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) Change this g(f(x))
11.
f(x)= 2x +
1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) Change this = 2(4x) + 1 = 8x + 1 g(f(x))
12.
f(x)= 2x +
1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) Change this = 2(4x) + 1 = 8x + 1 g(f(x)) g(f(x))
13.
f(x)= 2x +
1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) = 2(4x) + 1 = 8x + 1 g(f(x)) = g(2x + 1) g(f(x))
14.
f(x)= 2x +
1 g(x) = 4x Composite functions f(g(x)) or f(g(x)) = f(4x) = 2(4x) + 1 = 8x + 1 g(f(x)) = g(2x + 1) = 4(2x +1) = 8x + 4 g(f(x))
15.
f(x)= 3x +
4 g(x) = 2x Composite functions f(g(x)) or f(g(x)) = f(2x) g(f(x)) = 3(2x) + 4 = 6x + 4 g(f(x)) = g(3x + 4) = 2(3x +4) = 6x + 8
16.
f(x)= x2 – 4
g(x) = 3x Find f(g(x)) f(g(x)) = f(3x) = (3x)2 – 4 = 9x2 – 4 Key Question
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