Among the statements below about the function check the correct ones Select one

Question

Among the statements below about the function check the correct ones Select one or more :1.The domain off isn? Cross out undo 3.The targetoffisR2 cross out undo 5. The value of f at (0,0,0) is (0,0) 67(2,0,1)-- (2,-1) LL (2,0,1)-(-1,2). cross ou undo f(2,0, 1) = 1 9. The equation f(z,y, z)-(1,1) has a solution 1 10. The equation f(a, y,a) (0,0) has more than one solution undg cross out he equation f (D OI has no e t a one 11 f transforms the ag-axis of R3 into the z-axis of IR? :12 F transform s the 2 axis EM nt they axisofR- 13. f transforms the waxs of R Into part of the y axis of IR? solution: cross out cross 0ut cross out cros Check

Explanation / Answer

1. True. (x, y and z three variables) also look at the function definition R3 -> R2

2. False

3. True. (2 variables) also look at the function definition R3 -> R2

4. False

5. True

x = y = z = 0

so x+y2 = 0 and y-z2 = 0

(0,0,0) -> (0,0)

6. True.

x = 2, y = 0 and z = 1

so x+y2 = 2 and y-z2 = -1

f(2,0,1) = (2,-1)

7. False.

As explained above f(2,0,1) = (2,-1)

8. False

As explained above f(2,0,1) = (2,-1)

9. True

so x+y2 = 1 and y-z2 = 1

x = 1 - y2 and z = (y-1)0.5

so yes solution exists e.g. y = 1, x = 0, z = 0

10. True

x = - y2

y-z2 = 0

let y = 0, x = 0, z = 0

let y = 1, x = -1, z = 1

11. True

On x-axis, y=0 and z = 0

f(x,0,0) = (x+y^2, y-z^2) = (x,0)  

12. False (as explained above)

13. True

On z-axis, x = 0, y = 0

f(0,0,z) = (x+y^2, y-z^2) = (0,-z^2)  

only y-coordinate is non-zero so it is negative y-axis.

please upvote the answer as I have answered all the parts now.

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