An inverse function is the opposite of the original function. The Notation of an inverse function is , where the original function is f (x).
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Jetzt kostenlos anmeldenAn inverse function is the opposite of the original function. The Notation of an inverse function is , where the original function is f (x).
Only one-to-one Functions (where one value of the domain goes to only one value in the range) can have inverses.
One-to-one Functions are when one value of the domain goes to only one value in the range. This differs from one-to-many functions where one value of the domain can go to several values in the range
To find the inverse of a function, you need to
Replace the function Notation with y (eg f (x) become y)
Rearrange the function so that x is the subject
Replace the x with the inverse function notation (eg x becomes and y with x.
Find the inverse function of f (x) = 5x + 6
Find the inverse function of
There are several types of questions you can be asked involving inverse functions. The questions can ask you to use one or more methods.
This type of question is shown through , where x is then replaced with a constant such as, . To solve these questions, all xs are replaced with the Number in the function.
Solve
This type of question is shown through . To solve this type of question, you set the function equal to y and then rearrange the question to get x on its own.
When , find x when
You can be asked to find domains and ranges for inverse functions. The domain (set of input values) of the original function will be the range (set of possible output values) of the inverse function. The domain of the inverse function will be the range of the original function.
domain (Set of input values) | Range (Set of possible output values) |
Original function | Inverse function |
Inverse function | Original function |
Find the inverse of with a domain of . State the domain and range of .
Part 1) Finding the inverse.
There are two ways of drawing an inverse function:
1) Directly reflect the original function in the line y = x using your transformation of a graph skills.
2) By finding the inverse function and then plotting the x and y coordinates.
An inverse function is the reflection of the original function in the line y = x, therefore we can use the original line and the line y = x as the line of reflection.
Graphically show the inverse of f (x) = 2x + 4
1) The original function (red) depicted graphically
2) The original function (red) and the line of reflection, y = x (blue)
3) The inverse function (green) is obtained through reflecting the original function (red) in the line of reflection (x = y) (blue).
This method might be a bit more difficult when the original function has a variable raised to a power other than 1; for instance, quadratics
After finding the inverse function, you can plot the domain and range (meaning the x and y coordinates)
Plot the inverse function with the domain
x | 0 | 1 | 2 | 3 | 5 | ||
y | 0 | -3 | -4 | -3 | 0 | 5 |
Then, draw the inverse function by drawing a line through all the points and extending through.
The inverse function is the opposite of the original function.
Replace the function notation (e.g f(x)) with a y; 2) Rearrange the function so that x is on its own; 3) Replace the x with the inverse function notation (e.g. f-1(x)) and the y with an x.
j-1(x)=x+2
Any equation can be the inverse function as long as it has the inverse function notation at the start
When x is known, you substitute the value of x into the function and solve. If x is not known but the inverse function is set to a constant, you rearrange the inverse function to get x on its own.
What is an inverse function?
The inverse function is the opposite of the original function.
What notation signifies there is an inverse function?
f^-1(x)
What type of functions can have inverse functions?
One-to-one
What is the line of symmetry for inverse functions?
y=x
What are the two ways of finding out the line for the inverse function?
1) reflect the original function in the line of symmetry y = x; 2) find out the y coordinate by substituting an x value
Solve a^-1 (5) = x^2 + 2x?
35
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