Notation
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
Inverses
A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.
A function f -1 is the inverse of f if
<span><span>for every x in the domain of f, f<span> -1</span>[f(x)] = x, and</span><span>for every x in the domain of f<span> -1</span>, f[f<span> -1</span>(x)] = x</span></span>
The domain of f is the range of f -1 and the range of f is the domain of f<span> -1</span>.
Graph of the Inverse Function
The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
For number one the media is 22 and 5
Answer:
4 feet
Step-by-step explanation:
We start by subtracting the 6 from the 14, to get the leftover space on the wall, 8 feet. We then divide that by two, since if the painting is centered there will be two equally-sized spaces on either side of it. This means that X = 4 feet.
Answer:
C. (4,28)
Step-by-step explanation:
The substitution method requires you to input a specified number in place of a variable. In this case, the variable 'x' should be replaced by the number 4. Using the order of operations, we know that multiplication should be applied before subtraction. When we replace 'x' with 4, we get the equation 'y=8(4)-4'. Multiplying 8 and 4 gives us 32. If we subtract 4 from 32, we get 28. The answer ends up being 'y=28'.
That is the first part of our solution. What we are actually looking for is an ordered pair. We know ordered pairs are written in the form (x, y). First, we need to find the 'x'. The 'x' has been given to us from the beginning, it is 4. Next is the 'y'. This is what we needed to find using substitution. We ultimately concluded that the 'y' is equivalent to 28. Therefore our ordered pair is (4, 28), the letter choice C.
I hope this helped you and that I clearly elaborated on the answer choice.
