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 m1. The domain of f is RS 02 The domain of f is R2 3. The target of f is R2 4. The target of f is IR3 11 1 La 5. The value of f at (0,0,0) is (0,0) 6f(2,0,1) (2, -1) B7 7(2, 0, 1) -(-1,2) 8-f(2, 0, 1) = 1 | El 9. The equationz, y, z) = (1, 1) has a solution. 10. The equation f(x,y,z) = (0,0)has more thanone solution. 11f transforms the z-axis of R3 into the z axis of IR 12 f transforms the z-axis of IRS into the g-axis of R 13. / transforms the z-axis of R3 into part of the y-axis of R 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 = (1-x)0.5

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

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