Answer:
3.Injective
4. As the name suggests Invertible means “inverse“, Invertible function means the inverse of the function. Inverse functions, in the most general sense, are functions that “ reverse ” each other. For example, if f takes a to b, then the inverse, f -1, must take b to a. The inverse of a function is denoted by f-1
5. The graph of the inverse of a function reflects two things, one is the function and second is the inverse of the function, over the line y = x. This line in the graph passes through the origin and has slope value 1. It can be represented as; y = f -1 (x)
6. The horizontal line test is a convenient method that can determine whether a given function has an inverse, but more importantly to find out if the inverse is also a function. We say this function passes the horizontal line test.
7. When given a function, draw horizontal lines along with the coordinate system.
Check if the horizontal lines can pass through two points.
If the horizontal lines pass through only one point throughout the graph, the function is a one to one function.
Explanation:
3. To have an inverse, a function must be injective i.e one-one. Now, I believe the function must be surjective i.e. onto, to have an inverse, since if it is not surjective, the function's inverse's domain will have some elements left out which are not mapped to any element in the range of the function's inverse.
4. As the name suggests Invertible means “inverse“, Invertible function means the inverse of the function. Inverse functions, in the most general sense, are functions that “reverse” each other. For example, if f takes a to b, then the inverse, f-1, must take b to a. In other words, we can define as, If f is a function the set of ordered pairs obtained by interchanging the first and second coordinates of each ordered pair in f is called the inverse of f. Let’s understand this with the help of an example.
5. An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
In trigonometry, the inverse sine function is used to find the measure of angle for which sine function generated the value. For example, sin-1(1) = sin-1(sin 90) = 90 degrees. Hence, sin 90 degrees is equal to 1. A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.
The inverse function returns the original value for which a function gave the output.
If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.
Example: f(x) = 2x + 5 = y
Then, g(y) = (y-5)/2 = x is the inverse of f(x).
Note:
The relation, developed when the independent variable is interchanged with the variable which is dependent on a specified equation and this inverse may or may not be a function.
If the inverse of a function is itself, then it is known as inverse function, denoted by f-1(x).
6. In mathematics, the horizontal line test is a test used to determine whether a function is injective (i.e., one-to-one).
7. One-to-One Function. A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written 1-1. Note: y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test.