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To find the slope-intercept form of the given line (4x - 2y + 1 = 0), we need to solve for (y).
[4x - 2y + 1 = 0]
Subtract (4x) and add (1) to both sides:
[-2y = -4x - 1]
Divide both sides by (-2) to isolate (y):
[y = 2x + \frac{1}{2}]
Now, the equation is in the slope-intercept form (y = mx + b), where the slope (m) is (2) and the y-intercept (b) is (\frac{1}{2}). So, the slope is (2) and the y-intercept is (\frac{1}{2}).
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What is the relationship between the domains and ranges of a function and its inverse?
The domain of a function, f(x), is a set of real numbers (call them values of x) which corresponds to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range ( y- value). So the range is the set of real numbers that are values of the function. An inverse of a function f(x) is denoted by f-1(x) where -1 is NOT an exponent. The notation f-1 does not mean 1/f (so it looks like a neg 1 exponent but it is not. Math people know to read this as the inverse function). Any function that passes the horizontal line test (which intersects the graph of the function only once) has an inverse, also it is a one-to-one function. Any one-to-one function has a graph that passes the horizontal line test. A one-to one function is a function in which not two different pairs have the same second component. For this kind of functions (one-to-one functions), the domain becomes the range for the inverse and vv. It means that if a point (x, y) is on the graph of f, then the point (y, x) is on the graph of f-1. Ex: y or f(x) = x2 (the domain is the set of all real numbers. you can square positives, negatives, fractions etc. the range is only all reals greater than or equal to zero). The graph of f(x) = x2 does not pass the horizontal test, because it intersects the graph at two points, let's say (-3, 9) and (3, 9). Inverse functions have ordered pairs with the coordinates reversed. If we interchange x- and y-coordinates then we obtain (9, -3) and (9, 3) but these ordered pairs do not define a function. Thus this function does not have an inverse. But if we restrict the domain, for example the set of all positive numbers including zero, then we allow it to have one, and this inverse function f-1 is a reflection of the graph of f about the line y = x, where f(x) = x2 and its domain is {x| x ≥ 0}. The inverse of the above function is the square root of x. which I will abbreviate as sq rt the inverse function becomes f-1(x) = √x (in other words, f you limit yourself to real numbers, you cannot use any negatives in place of x for this inverse function. So the domain of the inverse is all reals > or = 0. If the inverse is to be a function you cannot have any answers which are negative. the relation would not pass the vertical line test. so the range is also only reals > or = zero).
What is the inverse of the function f(x) x 2?
It is difficult to be sure because the browser used for posting questions on this site is utter rubbish and strips out all mathematical symbols. If your question was f(x) = x + 2 then the inverse is f(x) = x - 2.
What are the inverses of hyperbolic functions?
If f(x)=y, then the inverse function solves for y when x=f(y). You may have to restrict the domain for the inverse function to be a function. Use this concept when finding the inverse of hyperbolic functions.
How are derivatives and anti derivatives related?
The derivative is the inverse of the integral. ∫ f'(x) dx = f(x) + C
How can the graph of f(x) 7 be obtained from the graph of y?
It cannot, in any sensible way.
How can you tell if a equation is inverse?
Graph that equation. If the graph pass the horizontal line test, it is an inverse equation (because the graph of an inverse function is just a symmetry graph with respect to the line y= x of a graph of a one-to-one function). If it is given f(x) and g(x) as the inverse of f(x), check if g(f(x)) = x and f(g(x)) = x. If you show that g(f(x)) = x and f(g(x)) = x, then g(x) is the inverse of f(x).
Function and inverse of function graph is the same?
In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.
What does the graph of f x is equal to Sin inverse bracket X plus 2 bracket look like?
It is not possible to draw a graph using this browser.
Given the function Fx you can get a picture of the graph of its inverse F-1y by flipping the original graph of Fx over the line?
y=x
What is the inverse of f of x equals 5x plus 4?
No, f(x) is not the inverse of f(x).
If f(x) and g(x) are inverse functions of each other shows the graph of f(g(x))?
f(g(x) = x, so it is the straight line through the origin, with a slope of 1.
Graph of an inverse proportion is an?
The graph of the function y(x) = 1/x is a hyperbola.
What is the inverse of the function f(x) 2 - x?
The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
What does the derivative graph mean?
I am assuming the you are talking about the graph of the derivative. The graph of the derivative of F(x) is the graph such that, for any x, the value of x on the graph of the derivative of F(x) is the slope at point x in F(x).
If f-1(x)g(x) inverse then the domain of g(x) the range of f(x)?
If f(x) is the inverse of g(x) then the domain of g(x) and the range of f(x) are the same.
If F(x) three x divided by 5 plus 3 is the inverse of F(x)?
If f(x) = 35/5 + 3 then its inverse is f(x) = 5/3*(x - 3).
What is the inverse of the function f(x) 4x 8?
The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
