What is the domain and range for the following function and its inverse? f(x) = x2 + 3 f(x) domain: f–1(x) domain:

Step-by-step explanation:

The domain of that function is all real numbers.  The x values will drop into negative infinity and will grow to positive infinity.

The range is found from the vertex form of a parabola, which is

where h indicates side to side movement of the vertex and k indicates up or down.  Our function has a +3 at the end of it and is positive (so it opens upwards), so the range is y ≥ 3.

To find the inverse of that function, switch the x and y coordinates and solve for the new y.  Let f(x) be y, then switch the x and y:

Now solve for the new y:

y = ±

To find the domain of a radical, set the radicand greater than or equal to 0 and solve for x (this is because the radicand cannot be a negative number or we are dealing with imaginary numbers and that's not what you want.  BTW, a radicand is the term under the radical sign).  

x - 3 ≥ 0  so   x ≥ 3.  The domain of the inverse is all real numbers greater than or equal to 3.

This is a sideways parabola (the inverse is), and it opens to the right starting at the x value of 3.  It will grow into positive values of y to infinity and will drop into negative values of y into negative infinity.

Just a little trick here to remember, and it ALWAYS holds true:  the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.  Look to our solution for your problem here and you'll see that it is true.

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

it alot will look like this 4.4