Determine i)the domain of the function, ii)the range of the function, iii)the domain of the inverse, and iv)the
range of the inverse.
-f(x)= -2x - 1
A)f(x): D is all real numbers, R is all real numbers; D is all real numbers, R is all real numbers

Question

Quizplus · Accepted Answer

i) The domain of the function is all real numbers, as there are no restrictions on the possible input values of x.
ii) The range of the function is also all real numbers, as the function can output any possible real number depending on the input value of x.
iii) To find the domain of the inverse, we need to switch the roles of the input and output variables and solve for the new output variable, which is now the input variable. So, we have y = -2x - 1, which we can solve for x to get x = (-1/2)y - 1/2. The domain of the inverse is therefore all real numbers since there are no restrictions on the possible input values of y.
iv) Similarly, to find the range of the inverse, we need to solve for the new output variable, which is now x. So, we have y = -2x - 1, which we can solve for y to get y = -2x - 1. The range of the inverse is therefore also all real numbers, as the inverse can output any possible real number depending on the input value of x. i) The domain of the function is all real numbers, as there are no restrictions on x in the equation.
ii) The range of the function is also all real numbers, as any value for x can be plugged in and produce a corresponding unique value of y (output).
iii) To find the domain of the inverse, we need to find the range of the original function. Since the range is all real numbers, the domain of the inverse is also all real numbers.
iv) For the range of the inverse, we switch the roles of x and y in the equation and solve for y:
y = -2x - 1
x = -2y - 1
(x+1)/(-2) = y
So the range of the inverse is also all real numbers.

Determine I)the Domain of the Function, Ii)the Range of the Function