Enter a Y (for Yes) or an N (for No) in each answer space below to indicate whether the corresponding function is one-to-one or not. You must get all of the answers correct to receive credit. (a) h (x) = |x| + 6 (b) k (x) = sin x for 0

Question

Layton Dalton

Mathematics

23 July, 19:55

Enter a Y (for Yes) or an N (for No) in each answer space below to indicate whether the corresponding function is one-to-one or not. You must get all of the answers correct to receive credit. (a) h (x) = |x| + 6 (b) k (x) = sin x for 0

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Answers (1)

Know the Answer?

Grant · Answer 1

a) No

b) No

Step-by-step explanation:

A function f is one to one if for all x, y in the domain of f, if x≠y then f (x) ≠f (y).

a) The domain here is not restricted. Assuming that the domain is the set of real numbers, h is not one to one. For example, take x=2 and y=-2. We know that x≠y, but h (x) = |2|+6=2+6=8 and h (y) = |-2|+6=2+6=8=h (x), hence h is not 1-1 because there exist some x, y such that x≠y but h (x) = h (y).

b) Reasoning as in a), take x=π/6 and y=5π/6. Both x and y are in the domain of sin (x) (in degrees, x=30° and y=150°) but sin (x) = sin (y) = 1/2. Hence k is not 1-1.