Question

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

Answer 1

a) No

b) No

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 .