What will undo a cube root? Answer: cubing. For example, cubing 2 to get 8 is the inverse operation of cube rooting 8 to get 2.
Vocabulary and Equations for Finding an Inverse of a Cubic Function and a Cube Root Function. Inverse Function: The inverse function f − 1 ( x ) of a function , if it exists, is a function that satisfies f ( f − 1 ( x ) ) = x for all in the domain of f − 1 ( x ) and f − 1 ( f ( x ) ) = x for all in the domain of .
The cube root is the reverse of the cube of a number and is denoted by ∛. For example, ∛216, that is, the cube root of 216 = 6 because when 6 is multiplied thrice with itself, it gives 216. In other words, since 63 = 216, we have ∛216 = 6.
The general equation for a cubed root function is f(x)=a3√x−h+k, where h is the horizontal shift and k is the vertical shift.
So, the inverse operation cube root of 8 will be 2. ⟹3√8=2.
What is the Inverse of 3x3 Matrix? The inverse of a 3x3 matrix, say A, is a matrix of the same order denoted by A-1 where AA-1 = A-1A = I, where I is the identity matrix of order 3x3. i.e., I = ⎡⎢⎣100010010⎤⎥⎦ [ 1 0 0 0 1 0 0 1 0 ] .
The cube function is increasing, so does not give the same result for two different inputs, and it covers all real numbers. In other words, it is a bijection, or one-to-one.
Unlike a square root, the result of a cube root can be any real number: positive, negative, or zero.
Horizontal Line Test
Let f be a function. If any horizontal line intersects the graph of f more than once, then f does not have an inverse.
Not every function has an inverse. It is easy to see that if a function f(x) is going to have an inverse, then f(x) never takes on the same value twice. We give this property a special name. A function f(x) is called one-to-one if every element of the range corresponds to exactly one element of the domain.
The inverse operation for the square of a number is the square root.
The multiplicative inverse (reciprocal) of the square root of two (i.e., the square root of 12) is a widely used constant.
The correct answer is: Square root.