Composite Functions
Composite functions are just combining two functions
fg(x) is a composite function of f(x) and g(x). It means do g(x) before f(x)
Mathematically this is done as below:
Mathematically this is done as below:
Domain and Range
The domain of a function is the range of x values the function covers
The range of a function is the range of y values the function covers
A common sign used here is ∈ ℝ
The range of a function is the range of y values the function covers
A common sign used here is ∈ ℝ
This means 'for all real values of ...' - this basically means, all values of a variable
For example:
For example:
Inverse Functions
An inverse function is a mirror image of a function through x = y
Take:
Take:
with a domain of x > 0, x ∈ ℝ and range f(x) > 0
Reflect in y = x
This gives you the inverse function of.
With a domain of x > 0 and a range of f(x) > 0
The domain for the inverse function is the range for the original function
The range for the inverse function is the domain for the original function
The range for the inverse function is the domain for the original function