Algebra of Functions

[Gerri]

Consider the following functions: f(x)=√(x-2) and g(x) =5

Please enter four ordered pairs that satisfy the function, f(x)=√(x-2)

Answers are: {(2,0), (3,1), (4,√2), (5,√3)}

I do not understand how they got these answers. Could someone please HELP!

Thank you,
Gerri

 

[JeffM]

Consider the following functions: f(x)=√(x-2) and g(x) =5

Please enter four ordered pairs that satisfy the function, f(x)=√(x-2)

Answers are: {(2,0), (3,1), (4,√2), (5,√3)}

I do not understand how they got these answers. Could someone please HELP!

Thank you,
Gerri

The way to think about a function is that it is a machine into which you feed a number (or vector) as input and which spits out a number (or vector) as output. Forget about vectors for now; I mentioned them just to give you a complete definition.

\(\displaystyle f(x) = \sqrt{x - 2}\) MEANS to take the number inside the parentheses, subtract 2 from it, and take the square root of the difference.

It is just a compact way of giving a rule about what to do to a number.

\(\displaystyle So\ f(2) = \sqrt{2 - 2} = \sqrt{0} = 0.\) If 2 is the input, then 0 is the output.

So if you were going to graph this point it would be (2, 0).

\(\displaystyle f(5) = \sqrt{5 - 2} = \sqrt{3},\ graphed\ at\ \left(5,\ \sqrt{3}\right).\) If 5 is the input to this function, then the square root of 3 is the output.

That's it. Now you understand functions. Like a toaster: you put bread in and get toast out.