how can the graph of f(x)= X^2-4X be used to obtain the graph of y=g(x)
??????
don't know can you help me out?
What is g(x)? The inverse function of f(x)?
http://www.uncwil.edu/courses/mat111hb/functions/inverse/inverse.html
To obtain the graph of y=g(x) from the graph of f(x), you need to find the inverse function of f(x).
The inverse function of f(x) can be found by swapping the x and y values and solving for y. So, let's switch the x and y in the equation:
x = y^2 - 4y
Now, solve this equation for y.
To solve for y, you need to complete the square. Here's how you can do it:
x = y^2 - 4y
x + 4 = y^2 - 4y + 4
x + 4 = (y - 2)^2
(y - 2)^2 = x + 4
Now, take the square root of both sides:
√((y - 2)^2) = ±√(x + 4)
Remember, when taking the square root, you need to consider both positive and negative values.
So the inverse function is:
g(x) = 2 ± √(x + 4)
Now, you can use this inverse function to obtain the graph of y=g(x).
To sketch the graph of y=g(x), you can follow these steps:
1. Start with the original graph of f(x) = x^2 - 4x.
2. Reflect the graph across the line y = x. This means that every point (x,y) on the graph of f(x) will become (y,x) on the graph of g(x).
3. Plot the resulting points on a coordinate plane to obtain the graph of y=g(x).
Alternatively, if you have the graph of f(x), you can simply reflect it across the line y = x to obtain the graph of y=g(x).
I hope this helps!