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The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix. The identity matrix that results will be the same size as the matrix A. Wow, there’s a lot of similarities there between real numbers and matrices.

Another important property is that not all functions will have inverses. You can use the horizontal line test to determine if the graph of a function will have an inverse. If there’s any point where, if you draw a horizontal line, it touches two or more points, then the graph will NOT have an inverse.

2 Answers. Characteristic for non-vertical “straight lines” is that they correspond with functions that can be prescribed by x↦ax+b where a,b are fixed real numbers. This tells us that such linear functions have an inverse if a≠0.

Key Steps in Finding the Inverse of a Linear Function

1. Replace f ( x ) f/left( x /right) f(x) by y.
2. Switch the roles of x and y, in other words, interchange x and y in the equation.
3. Solve for y in terms of x.
4. Replace y by f − 1 ( x ) {f^{ – 1}}/left( x /right) f−1(x) to get the inverse function.

The inverse function of a straight line is also a straight line, except for the case where the straight line is a perfectly horizontal line, in which case the inverse is undefined. For example, the straight line equation given by y=2x-3 has as inverse the function, y=12x+32.

An inverse curve can be plotted as a straight line, which has the general form y = mx + c, where m is the gradient and c is the y-intercept, by calculating the inverse or “reciprocal” of the x coordinates and then replotting them against the original y coordinates.

A relationship between two variables that move in opposite directions is called a negative relationship or an inverse relationship. A line that slopes downward shows a negative relationship.

Answer: The multiplicative inverse or reciprocal of 3/5 is 5/3.

A set has the inverse property under a particular operation if every element of the set has an inverse. An inverse of an element is another element in the set that, when combined on the right or the left through the operation, always gives the identity element as the result.