(a)
To calculate: find domain and range.
Domain:
Given information:
Formula used: trigonometry
Calculation: Domain
Inner function: the arcsine function can only take in values in the domain
Outer function: the sine function can take in any values, so the domain of the function as a whole is limited solely by the inner function. Thus the domain of the function is
Range
Inner function: the sine function only outputs values in the range
Outer function: considering the output of the arcsine function, the only values that will be output are
This is the range of the function overall.
(b)
To calculate: find domain and range.
Domain:
Given information:
Formula used: trigonometryCalculation: Domain
Inner function: both the sine and arcsine function can only take in values in the domain
Range
Let us consider the endpoints of the domain to give us a clue about the nature of the range of the function. At
At
In fact, at every value of
Therefore, the range of
(c)
To calculate: find domain and range.
Domain:
Given information:
Formula used: trigonometry
Calculation:
Domain:
Inner function: the sine function can take in any value of
However, it outputs only
Outer function: the arcsine function can take in values in the domain
Since the inner function cannot output any value that the outer function cannot evaluate, the domain of the function is thus
Range:
Inner function: the sine function outputs only
Outer function: since the output of the inner function is the entire domain of the outside function, the range of
(d)
To calculate: find domain and range.
Domain:
Given information:
Formula used: trigonometry
Calculation:
Domain:
Inner function: the arccosine function can take in values in the domain
Outer function: the arcsine function can take in values thus the domain as a whole is limited only by the inner function, making the overall domain
Range:
Inner function: the arccosine function only outputs values of
Outer function: in the domain
(e)
To calculate: find domain and range.
Domain:
Given information:
Formula used: trigonometry
Calculation:
Domain:
Inner function: the arccosine function can take in values of x but will output the range
Outer function: given the input
Thus, the domain is
Range:
Inner function: the sine function only outputs values of
Outer function: when presented with the domain
Chapter 4 Solutions
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
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- Example 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet. (a) What is the velocity at time t? (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) What is the acceleration at time t? (f) What is the acceleration after 3 s?arrow_forwardConstruct a table and find the indicated limit. √√x+2 If h(x) = then find lim h(x). X-8 X-8 Complete the table below. X 7.9 h(x) 7.99 7.999 8.001 8.01 8.1 (Type integers or decimals rounded to four decimal places as needed.)arrow_forward
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