SOLUTION: The book asks for this group of problems to be tested to see if the function is one-to-one. The book gives an explanation of this test, but it is very short and of little help. Can

Question 83566This question is from textbook PreCalculus - A Graphing Aproach
: The book asks for this group of problems to be tested to see if the function is one-to-one. The book gives an explanation of this test, but it is very short and of little help. Can you explain the testing process a little better? For instance, the example the book gives is f(x) = (sqrt x) + 1. It then assigns nonnegative real numbers a & b such that f(a) = f(b). In the end, a = b. How does this work with real problems like (3x+4)/5?This question is from textbook PreCalculus - A Graphing Aproach

Answer by nilan(10) (Show Source):
You can put this solution on YOUR website!
The definition of one to one function says
A function is said to be one to one if f(a)=f(b) then a=b
It means that no any deferent values map to one value
So if you want to prove a given function is one to one, you have to do the general proof
It means, getting arbitrary two values called a,b and suppose that f(a)=f(b) and show that finally a=b
It is enough to give a concrete example to show a given function is not one to one.
To show a function is one to one
F(x) = (3x+4)/5
Let a and b are any real numbers and suppose
f(a) =f(b)
then
(3a+4)/5 = (3b+4)/5
3a+4=3b+4
3a=3b
a=b
so f(x) is one to one
To show a function is not one to one
f(x) = square(x)
In the first site, we see that this is can’t be one to one since 1 and -1 map to 1
So, in this case you can give this concrete example to how this is not one to one
f(1)=f(-1) = 1
Two deferent values map to a single value, hence this is not one to one.