# Domain and range?

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#1
I'm doing A level AQA Maths and one of the beginning modules is focused on the domain and range of a function and its inverse function. I understand that the domain is the input values and the range is the output values but I'm so confused as to how to work them out?
For example;
1. Given f(x) = *square root of* x, +1 (outside square root) , x *greater than or equal to* 0
a) Questions asks to sketch graph of f(x)
b) FInd the inverse function ; which I've worked out to be (x-1)^2

This is the part I don't understand....
c) State the domain of f^-1(x)

I know that the domain of the inverse is the range of f(x), but I seriously have no clue how you find the range in the first place

0
5 years ago
#2
You are probably already aware that an inverse function is the original function reflected in the y=x line.
Whe you reflect something on the line y=x you interchange the x and y coordinates. So a point (3,2) reflected in the line y=x becomes (2,3)
So in terms of domain and range - the domain of the function is the range of the inverse function
And the range of the original function is the domain of the inverse function due to this property of reflecting in the line y=x
The range of the function is all the f(x) values that can be obtained from the set of x values allowed - the domain
The domain in this case is x is greater than or equal to 0
So what are all the values that can be obtained when we out these values of x into the function? What is the minimum value of a square bracket like (x-1)^2
What is the maximum value - if there is one
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#3
I wrote down the whole question, and that's all there was to it.
I'm afraid I didn't understand most of what you said, apart from the information I said I already understood.

I feel like this is something really simple and I'm just making it a lot harder than it is.
0
5 years ago
#4
For this question find the range of f(x)
And then that answer that you get is the domain of f^-1(x)
1
#5
I think I've worked out the range as f(x) *greater than or equal to* 1.
Do you literally just sub in the domain for f(x) into the equation of f(x) to find the range?
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5 years ago
#6
(Original post by megan.gurr)
I think I've worked out the range as f(x) *greater than or equal to* 1.
Do you literally just sub in the domain for f(x) into the equation of f(x) to find the range?
No you can just say that the range of f(x) which you just worked out to be x>=1 is the domain of f^-1(x)
It's that simple
0
#7
Thank you!
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