Question

Which table shows the domain and range of the function y = cos^(-1)(4x)?

a)x | -1 | -0.5 | 0 | 0.5 | 1
y | 0 | 1.047 | 1.571 | 2.094 | 3.142

b)x | -0.5 | 0 | 0.5 | 1 | 1.5
y | 0 | 1.047 | 1.571 | 2.094 | 3.142

c)x | -1 | -0.5 | 0 | 0.5 | 1
y | 3.142 | 2.094 | 1.571 | 1.047 | 0

d)x | -1 | -0.5 | 0 | 0.5 | 1
y | 3.142 | 2.094 | 1.571 | 1.047 | 0

Answer 1

The table that shows the correct domain and range for the function y = cos^-1(4x) is option (a), which accommodates the domain of x between -0.25 and 0.25 and the range of y between 0 and π.

Step-by-step explanation:

The function given is y = cos-1(4x), which is the inverse cosine function or arccosine function. The domain of the arccosine function is the set of values that x can take such that the argument of the cosine function lies within the interval [-1, 1]. Since the argument here is 4x, for y = cos-1(4x) to be valid, 4x must lie within [-1, 1]. This means x must lie within [-0.25, 0.25]. The range of the arccosine function is the set of possible output values, which for the inverse cosine function is [0, π]. Therefore, option (b) with x values outside the interval [-0.25, 0.25] is incorrect. Option (c) and (d) show identical x and y-values but reversed. Option (a) shows the correct domain and range, as the domain of x is between -0.25 and 0.25 (scaled to integers here for simplicity), and y values are between 0 and π, inclusive.