Composite And Inverse Functiond

Question 1

What’s a function

Answer 1

Is an operation that takes numbers and maps each one to only one number.

f(x) = x^2

f : x -> x^2

Question 2

Set of starting big numbers are called ___ in functions and the numbers they become is the ______ or ______

Answer 2

Domain

Range or image

Question 3

If x can take any real value it’s usually written

Answer 3

x E R

E looks dif look page 34

Question 4

One to one function

Answer 4

Maps one element in the domain to one element in the range

Question 5

A many to one function

Answer 5

Maps more than one element in the domain to one element in the range

Question 6

One to many mapping’s can

Answer 6

Take an element in the domain to more than one element in the range

By definition it’s not a function

Question 7

Functions can be combined

Answer 7

This is called a composite function.

Written fg(x) this means do g first then f

If you get f^2(x) it means ff(x)

Question 8

Which functions have inverses?

Answer 8

One to one functions only.

Question 9

What is an inverse function

Answer 9

It does the opposite of the function, it maps and element in the range to an element in the domain.

F^-1f(x)

The domain of the inverse is the range of the function.

Question 10

Calculating an inverse function

Answer 10

Make f(x) to y

Then make x the subject of the equation

Replace y with x and x with f^-1(x)

Swap the domain and the range

To find range of function from domain put smallest number of domain into function…

Inverse function so inverse the domain to become range of inverse function…

Question 11

You might have to draw the graph of the inverse

Answer 11

The inverse of a function is its reflection in the line x=y