Look at the function f(x)=x^2-2. which of the following describes the domain and range of the function and its inverse?

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3