one-to-one functions: exerise #13 (how is g(x) = sqrt{x} one-to-one?)

[Illvoices]

so i was told to determine whether the function is one-to-one for question number 13 but they got yes as an answer, could someone tell me how'd they get yes when a the you cant have the same square root of a different number for question 13

13)g(x)=square root of (x)

 

[Harry_the_cat]

so i was told to determine whether the function is one-to-one for question number 13 but they got yes as an answer, could someone tell me how'd they get yes when a the you cant have the same square root of a different number for question 13

13)g(x)=square root of (x)

\(\displaystyle y = \sqrt {x}\)

Ask yourself two questions to test for a 1-1 function.
1. If you put in any one value of x from the domain (here the domain is all non-negative numbers), do you only get one value for y?
and
2. If you put in any one value of y from the range (here the range is all non-negative numbers), do you only get one value for x?

If the answer is yes to both questions, then it is a 1-1 function.

Ask yourself these questions for the function \(\displaystyle y = \sqrt {x}\). What answers do you get?

 

[Illvoices]

thank you for replying to this problem and i guess if you put in a 2 in for the x value it wont make a difference but what does this mean, could it be that g is going to make x look like the square root or does g stop playing a role in this question.
note: g is only a letter in this problem, what does it represent and could it be changed to a value?

 

[mmm4444bot]

g(x) doesn't mean g times x.

The letter g is the name they picked for the function.

The symbol g(x) is another way of writing y.

y = sqrt(x)

g(x) = sqrt(x)

Same thing.

Therefore, g(x) is the variable y. It represents the output of function g when x is the input.

When we write g(x) instead of y, it's called "function notation".

g(x) = sqrt(x)

When we let x=9, then function g returns the square root of 9.

Therefore, g(9) = 3

g(9) = 3 tells us that 9 went into the function, and 3 came out.

Are you familiar with the graph of y = sqrt(x)?

Does it pass the Horizontal Line Test?

If it does, then function g is one-to-one. :cool:

 

[Illvoices]

okay thanks bot i got the point.