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# Function questions watch

1. State whether the following mappings are functions, and is they are one-one, one-many,many-one or many-many relations.

a) x^2+y^2=1
b) y=x^4
c) y = √x (x ≥0)

For the first mapping it is not a function but I am not sure what type of relation it is. In addition, for the second I think it is a one-many relation and the third I am not sure altogether.

Then : find fg(x) and gf(x)
When f(x) = x^2 and g(x) = 2x+3

Would fg(x) be (2x+3)^2;
because f(g(x)) then substitute the value of g into f

Likewise gf(x) = 2x^2 +3
because g(f(x)) then substitute the value of f into g= 2x^2 +3

Finally,
If f(x) =x^2+4 find the inverse function of f^-1(x).
For this would I find the inverse of f^-1(x) or the first function?

In either case the inverse function of f(x)=x^2+4 = ±√x-4
Or for the second function f^-1(x) = fx

Are these correct?
2. (Original post by AliceAM342)
State whether the following mappings are functions, and is they are one-one, one-many,many-one or many-many relations.

a) x^2+y^2=1
b) y=x^4
c) y = √x (x ≥0)

For the first mapping it is not a function but I am not sure what type of relation it is.
Correct, it's not a function. But note that a single y value (between -1 and 1) corresponds to two distinct x values (between -1 and 1). Similarly, a single x value corresponds to two y values. So the relation is...?

In addition, for the second I think it is a one-many relation
Not quite. A single x value corresponds to a single y value. But, a single y value corresponds to two x values.

and the third I am not sure altogether.
Same procedure, how many values does a chosen x output? How many values does a chosen y output?

When f(x) = x^2 and g(x) = 2x+3 ... Would fg(x) be (2x+3)^2 ... Likewise gf(x) = 2x^2 +3
These are correct.

Finally,
If f(x) =x^2+4 find the inverse function of f^-1(x).
For this would I find the inverse of f^-1(x) or the first function?
In either case the inverse function of f(x)=x^2+4 = ±√x-4
That's fine.
3. (Original post by RDKGames)
Correct, it's not a function. But note that a single y value (between -1 and 1) corresponds to two distinct x values (between -1 and 1). Similarly, a single x value corresponds to two y values. So the relation is...?

Not quite. A single x value corresponds to a single y value. But, a single y value corresponds to two x values.

RDKGames

Same procedure, how many values does a chosen x output? How many values does a chosen y output?

These are correct.

That's fine.
For the first mapping would it be a many-many relation because , as you said, there is a single y value to two x values and a single x value to two y values, this mapping has single y and x values so would the other value then correspond at two of the value?
For the second mapping would it be a one-many relation , which is not a function,?
And for the third mapping would it be a one-many relation again (not a function) because there is a singular y value and multiple x values?

4. (Original post by AliceAM342)
For the first mapping would it be a many-many relation because , as you said, there is a single y value to two x values and a single x value to two y values, this mapping has single y and x values so would the other value then correspond at two of the value?
Correct, but I don't understand your question.

For the second mapping would it be a one-many relation , which is not a function,?
Not quite.

And for the third mapping would it be a one-many relation again (not a function) because there is a singular y value and multiple x values?
Not quite. One-many means a single x outputs multiple y.
5. Would the second mapping be a many-one relation, because there is a single y value to 4 x values.
For the third mapping would it be a many- one relation, because there is a single y value to 2 x values?

RDKGames
6. (Original post by AliceAM342)
Would the second mapping be a many-one relation, because there is a single y value to 4 x values.
Yes it's many-one, but a single y only corresponds to two x values, not four.

For the third mapping would it be a many- one relation, because there is a single y value to 2 x values?
No. Think about what you're saying - can you give an example where two different values output a single value for ? More importantly, do you know how this function even looks like?
7. I’m sorry I am confused by the last mapping and cannot answer your question. I had been doing mappings, functions etc. But not with equations until now, only a series of numbers for the domain and range.

I thought that there were 4 x values because the second mapping has x^4.

For the third mapping I am lost, sorry 😯

RDKGames
8. (Original post by AliceAM342)
For the third mapping I am lost, sorry 😯

RDKGames
It's a one-one mapping. For each you get a single output, and each corresponds to a single input.
9. (Original post by RDKGames)
It's a one-one mapping. For each you get a single output, and each corresponds to a single input.
Thank you very much for your help, I really appreciate it. I understand (mainly) the third mapping.

I will do some research to understand this topic more.
Thank you 😊 RDKGames

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