We expect to see a ___ for the graph of a composition of a function and its inverse function, if the domain of each is all real numbers.
line
We expect to see a straight line with a slope of 1 for the graph of a composition of a function and its inverse function, if the domain of each is all real numbers.
This is because when we compose a function with its inverse, we are essentially asking what happens when we apply the function and then undo the effect of that function? Since the function and its inverse function undo each other’s effect, the output of the composition is the input value itself.
So, if we plot the composition of a function and its inverse function on a graph, we will get a straight line with a slope of 1, which represents all the points where the input and output values are equal. This line is commonly referred to as the line of symmetry, and it bisects the graph into two mirror images of each other.
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