Not all attributes have train station functions. The graph that inverse attributes are reflections end the line y = x. This means that each x-value have to be matched to one and also only one y-value. Features that accomplish this criteria are referred to as one-to one functions.

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DEFINITION of ONE-TO-ONE:

A function is claimed to be one-to-one if each x-value synchronizes to specifically one y-value.

A duty f has actually an inverse function, f -1, if and also only if f is one-to-one.


A fast test because that a one-to-one duty is the horizontal line test. If a horizontal heat intersects the graph the the duty in more than one place, the attributes is not one-to-one.

HORIZONTAL line TEST:

A function f is one-to-one and also has one inverse duty if and only if no horizontal heat intersects the graph that f at an ext than one point.


Step 1: sketch the graph of the function.

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Step 2: use the Horizontal line Test.

Visualize multiple horizontal lines and look for places where the graph is intersected more than once.

No horizontal line intersects the graph in much more than one place and thus the duty has an inverse.

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step 1: map out the graph of the function.

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Step 2: use the Horizontal line Test.

Visualize multiple horizontal lines and also look for places where the graph is intersected an ext than once.

number of horizontal lines intersect the graph in 2 places. Hence the role is not a one-to-one and also does not have actually an inverse.

Also an alert that if the ordered pairs space switched, this outcomes in repeating x-values and also a duty cannot have repeating x-values.


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