How would I go about finding the domain and range of 3cos(3x+π) = 4? Thanks
You have given me an equation, not a function
The concept of domain and range applies to functions
was your function
f(x) = 3cos(3x+π) - 4 ?
if so , the domain is any real number
the range is -1 to -7
were you looking for a solution to your equation?
cos(3x+π) = 4/3
BUT, the cosine of anything lies between -1 and 1
so your equation has no solution.
The question(s) were as follows:
Given: f(x) = 3cos(3x+π) - 4 (as you thought)
Find:
a) the inverse of F(x)
b) the domain and range of F(x)
c) the domain and range of F -1(x)
I got cos-1[(x-4)/9] - π =y for the inverse, although I'm not sure I did the problem right (I set x to y and y to x and then solved for y).
For cos(3x+π) = 4/3, don't I have to finish solving cos(3x+π) before I decide that there is no solution? I have been doing these and other problems for so long today that I am gettin more confused - not less, lol! Thanks for your help.
To find the domain and range of the equation 3cos(3x+π) = 4, we need to analyze the properties of the trigonometric function cosine (cos) and the given equation.
1. Domain:
The domain refers to the set of all possible values that the independent variable, in this case, 'x', can take. Since cosine is defined for all real numbers, there are no restrictions on the domain of the function.
Thus, the domain of the equation 3cos(3x+π) = 4 is (-∞, +∞) or all real numbers.
2. Range:
The range represents the set of all possible values that the dependent variable, in this case, 'y' or 'cos(3x+π)', can take. To find the range, we need to consider the range of cosine function itself.
The range of the cosine function is typically between -1 and +1. However, applying a coefficient of 3 to the function stretches it vertically by a factor of 3.
The given equation is 3cos(3x+π) = 4, which implies that the vertical shift of the cosine function is raised to 4 units.
So, the range of the equation 3cos(3x+π) = 4 is [1/3, 4/3].
In summary:
- The domain of 3cos(3x+π) = 4 is all real numbers (-∞, +∞).
- The range of 3cos(3x+π) = 4 is [1/3, 4/3].