how can the inverse of a function be the same?
449328
The inverse for a function of x is just the same function flipped over the diagonal line x=y (where y=f(x)). So, if you graph a function, and it looks like it mirrors itself across the x=y line, that function is an inverse of itself.
418608
Inverse function definition. An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing.
1146356
So in summary, the inverse of any constant function will always be a vertical line which is not a function. Therefore, every constant function has no inverse function!
1055863
For f(x)=x2 , we ghave f(−1)=f(1) (for example), so there is no inverse function.
733721
For a function to have an inverse, each element y ∈ Y must correspond to no more than one x ∈ X; a function f with this property is called one-to-one or an injection. If f −1 is to be a function on Y, then each element y ∈ Y must correspond to some x ∈ X.
1211269
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=3√x+2 f - 1 ( x ) = x + 2 3 is the inverse of f(x)=x3−2 f ( x ) = x 3 - 2 .
179163
Given a function, say f(x), to find the inverse of the function, we first change f(x) to y. Next, we change all x to y and y to x. and then we solve for y. The obtained solution for y is the inverse of the original function.
1318
For example, find the inverse of f(x)=3x+2. 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 f^{-1} f−1f, start superscript, minus, 1, end superscript, must take b to a.
570007
The cube function is increasing, so does not give the same result for two different inputs, plus it covers all real numbers. In other words, it is a bijection, or one-to-one. Then we can define an inverse function that is also one-to-one. For real numbers, we can define a unique cube root of all real numbers.
391129
In the math example, the steps are to multiply by 8 and take the cube root. The inverse operations in reverse order are to cube and divide by 8. Take x, cube to get x3 and divide by 8 to get x3/8. This x3/8 is called the inverse function and is written as f-1 (x).
1392666
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=5x+2 f - 1 ( x ) = 5 x + 2 is the inverse of f(x)=5x−2 f ( x ) = 5 x - 2 .
255630
Yes, they are the same. You just have to factor the (x2 - 1) in the numerator of f(x) and cancel out the (x + 1).
1281417
The inverse of a function ƒ is a function that maps every output in ƒ's range to its corresponding input in ƒ's domain. We can find an expression for the inverse of ƒ by solving the equation 𝘹=ƒ(𝘺) for the variable 𝘺. See how it's done with a rational function.
678491
['Switch f(x) and x. When you switch f(x) and x, you get. (Note: To make the notation less clumsy, you can rewrite f(x) as y and then switch x and y.)', 'Change the new f(x) to its proper name — f–1(x). The equation then becomes.', 'Solve for the inverse. This step has three parts:']
1229984
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=3√x−8 f - 1 ( x ) = x - 8 3 is the inverse of f(x)=x3+8 f ( x ) = x 3 + 8 .
1223637
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=−x6−76 f - 1 ( x ) = - x 6 - 7 6 is the inverse of f(x)=−6x−7 f ( x ) = - 6 x - 7 .
1428652
Answer and Explanation: The inverse of log10 (x), denoted log(x), is 10x.