I have some problems that I need help with please. Thanxs!
Find the domain of the function.
1. f(x)=-8x-2
Given fuctions f and g, perform the indicated operations.
2. f(x)=4x-9 g(x)=7x-3
find f - g.
Given the functions f and g, determine the domain of f + g.
3. f(x)=2x/x-3 , g(x)=3/x+6
I will be happy to critique your work or thinking on this.
Sure! I'd be happy to help you with your problems. Let's go through each question step by step.
1. To find the domain of the function f(x) = -8x-2, you need to determine all the possible values of x that make the function defined. In this case, there are no restrictions or limitations on the expression -8x-2, so the domain is all real numbers (-∞, ∞).
2. To find the difference between two functions f(x) = 4x-9 and g(x) = 7x-3, you simply subtract the corresponding coefficients. In other words, for each x term, subtract the g(x) coefficient from the f(x) coefficient. In this case, f - g = (4x - 7x) + (-9 - (-3)) = -3x - 6.
3. To find the domain of the sum of two functions f + g, you need to consider the domain restrictions of both functions. In this case, we have f(x) = 2x / (x - 3) and g(x) = 3 / (x + 6). The domain of f(x) is all real numbers except x = 3, since dividing by zero is undefined. Similarly, the domain of g(x) is all real numbers except x = -6. Therefore, to find the domain of f + g, we need to exclude both x = 3 and x = -6. So the domain of f + g is all real numbers except x = 3 and x = -6.