Function Operations
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6.3 Function Operations
Transcript of Function Operations
6.3 Function Operations
Review: What is a function?
A relationship where every domain (x value has exactly one unique range (y value).
Sometimes we talk about a FUNCTION MACHINE, where a rule is applied to each input of x
Function Operations
xgxfxgf )( :Addition
xgxfxgf :tionMultiplica
xgxfxgf :nSubtractio
0xg where :Division
xg
xfx
g
f
Adding and Subtracting Functions
45
)122()83(
)(
x
xx
xgxfxgf
g - f and g f Find
.122g and 83fLet
xxxx
20
)122()83(
)(
x
xx
xgxfxgf
When we look at functions we also want to look at their domains (valid x values). In this case, the domain is all real numbers.
Multiplying Functions
1
)1)(1()(23
2
xxx
xxxgxf
g f Find
.1g and 1-fLet 2
xxxx
In this case, the domain is all real numbers because there are no values that will make the function invalid.
Dividing Functions
1)1(
)1)(1(
1
12
xx
xx
x
x
xg
xf
g
f Find
.1g and 1-fLet 2 xxxx
In this case, the domain is all real numbers EXCEPT -1, because x=-1 would give a zero in the denominator.
Let’s Try Some
)( Find xgxf
.15g and 1-5fLet 2 xxxx
)( Find xgxf What is the domain?
Composite Function – When you combine two or more functions
The composition of function g with function is written as xfgxfg
1
21. Evaluate the inner function f(x) first.
2. Then use your answer as the input of the outer function g(x).
Example – Composition of Functions
xfgxfg
2)2()2( xxgxg
49)7( 2
5 Find . and 2xfLet 2 fgxxgx Method 1:
2255 fg
Method 2:
xfgxfg
)25(5 gfg
49)7( 2
)7(g
