Functions Flashcards
How else would you write fg(2)?
f[g(2)]
What are the steps of finding an inverse function?
1) Let y=f(x)
2) Swap x and y
3) Make y the subject
4) Write as f^-1 (x)
What is the domain?
x values on a graph
the set of all possible inputs
What is the range?
y values on a graph
the set of all possible outputs
What are examples of 1 to 1 functions?
f(x) = 2x + 3
f(x) = e^x
What is an example of a many to one function?
f(x) = x^2
What is a one-to-one function?
for each value of x, there is only one value of y
What is a many-to-one function?
many values of x that will give 1 value of y
put in a value of x and get 1 value of y
What is a one-to-many function?
1 x value could give you multiple y values
eg x=y^2
What is a many-to-many function?
many values of x that give many values of y
eg a graph that is a circle
Why can a function never be one-to-many or many-to-many?
Not functions because you put in 1 value of x and get 2 values of y
-supposed to get 1 output
What does a function have to be in order to have an inverse?
A one-to-one function
If a function is many-to-one why can it not have an inverse?
Because when its reflected in the line y=x, it would become a one-to-many which is not a function
What do you do when drawing the graph IxI ?
(modulus of x)
Reflect the “negative part” of y=x in the x axis
