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Functions Rules, Types of Functions, Inverse of a Function, Operation of…
Functions Rules
Codomain (All possible functions output values)
Domain (all possible functions input values)
All factors in domain must be assigned
It can't assigned twice
Range (All actual output values)
Example:
If you want to find the image of the functions!!
The rule is in this picture is f(x)= 2x+1
f(1)= 3
Types of Functions
Onto Function
f:X → Y f(X) = Y
Image must be equal to range
Identity Function
I=A→ A I(x)=x
One to one Function 1-1
f:A → B for any a1,a2 ∈ A
Image of each element in the domain is different than one other
Into Function
f(A)≠B
At least one number in B must stay exposed
Constant Function
Output value is the same for every input value
There is no factors like
x
Linear Function
f(x)=ax+b
Its graph is a line
Piecewise Function
It's the combination of the equations
Inverse of a Function
Its shown as f(x)=f^-1
ax+b/cx-d
→
dx+b/cx-a
It must be onto and 1-1
ax+b → x-b/a
Firstly x+b to x-b
Then a to denominator
Operation of the Functions
Subtract Functions
(f-g) (x)=f(x) - g(x)
Multiply Functions
(
f.g) (x)=f(x) . g(x)
Add Functions
(f+g) (x)=f(x) + g(x)
Divide Functions
(
f/g) (x)= f(x) / g(x)
Line Test Of Graphs
Horizontal Line Test
It looks that the graph is one to one or not
Vertical Line Test
It looks that the graph is function or not
