Question

if f(x)=root(36-x^2) then the range of values of f is given by ?

Answer 1

@waterineyes Will i have to put root(36-x^2)not equal to zero ?

Answer 2

This time you have to find range..

For that put f(x) = y


Now :

\[y = \sqrt{36 - x^2}\]

Answer 3

i got this how to solve it ?

Answer 4

Now convert this in terms of y :

\[y^2 = 36 - x^2 \implies x^2 = 36 - y^2 \implies x = \sqrt{36-y^2}\]

Answer 5

I got this too,Next ?

Answer 6

Now put :

\(36-y^2 \ne 0\)

And now find y..

Answer 7

y is not equal to plus minus 6

Answer 8

{y:0<=y<=36} < Can this be the answer ?

Answer 9

The other options are,

{y:-6<=y<=6}
{y:0<=y<=6}
{y:-6<=y<=0}

Answer 10

36 or 6??

Answer 11

@waterineyes Yes ?

Answer 12

The first one

Answer 13

{y:0<=y<=36}

Answer 14

Should be the answer ^

Answer 15

@waterineyes Please help :'(

Answer 16

@waterineyes What ?

Answer 17

See from here :

\[y = \sqrt{36-x^2}\]

y cannot take negative values, so y cannot be : -6, -5, -4 , -3, -2, -1...

Answer 18

So I think \(0 \le y \le 6\)..

Answer 19

But y is not equal to +-6

Answer 20

@waterineyes ?

Answer 21

Sorry, I may be wrong..

I don't know..

Answer 22

@campbell_st Please help ?

Answer 23

@waterineyes Thanks Alot for your help.

Answer 24

Gotta go..

Good Night hba..

Answer 25

@waterineyes Good night :)

Answer 26

ok.... you can't take the square root of a negative number...does that make sense...?

Answer 27

No.

Answer 28

\[36 -x^2 \ge 0\]

Answer 29

I am done with this :(

Answer 30

Because no one is helping me out :(

Answer 31

start with the basics.... can you take the square root of a negative number...?

Answer 32

Yes.

Answer 33

It is just gonna turn complex

Answer 34

ok.... what in

\[\sqrt{-4} = ?\]

Answer 35

so 2i

Answer 36

I mean +- 2i

Answer 37

ok... so from what you are saying you can input (the domain) any value of x....is that correct...

Answer 38

then you need to think about what output(the range) you will get...

Answer 39

Yes.

Answer 40

Ok so I have worked it out and the range y should not be equal to +-6

Answer 41

but the way I read this question, you are asked for the range, based on the set of real numbers...

Answer 42

no... what you have worked out with + - 6 is the input..... from the set of real numbers....

now you have to find the output...

start with the largest input value 6 what is the output..?

Answer 43

positives and negatives squared give the same answers

Answer 44

0

Answer 45

For 6

Answer 46

ok... so input the smallest value 0... whats the output...

Answer 47

36 ?

Answer 48

@campbell_st ?

Answer 49

umm nope isn't it

\[\sqrt{36 - 0} = 6\]

Answer 50

so the output ranges from 0 to 6

Answer 51

Oh Yeah sorry its 6

Answer 52

So C is the answer ?

Answer 53

you didn't post a list of your answer choices....

but basically the range(output) is determined by the domain(input)

Answer 54

{y:0<=y<=6}

Answer 55

@campbell_st Is this correct ^^ ?

Answer 56

that looks like it

Answer 57

thanks :D