Question 894815: Inverse Functions.
1)Explain how to find the inverse of a function when the function is given in each of the following formats.
a)As a table of inputs and outputs.
b)As a graph.
c)As a equation.
2)Explain how to determine if two functions in equation form are inverses of each other and give a sample pair of functions for your classmates to practice determining if they are functions.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let's take a look at how we derive inverse functions by equation.
if y = 5*x, then you find the inverse qeuation by replacing y with x and x with y and solving for y.
y = 5*x becomes x = 5*y
solve for y to get y = x/5.
the inverse equation of y = 5x is y = x/5.
that's by equation.
now by table.
take the same equation of y = 5x and make a table.
you get:
(x,y) = (1,5), (2,10), (3,15), (4,20), etc.
now replace x with y and replace y with x to get:
(x,y) = (5,1), (10,2), (15,3), (20,4), etc.
the first table gets you the equation of y = 5x.
the second table gets you the equation of y = x/5.
all you do is interchange the x valuea and the y values and you have a table for the inverse equation.
graphically, you would plot the (x,y) points for y = 5x.
for each (x,y) point, you would plot the corresponding point of (y,x).
if you then draw the line y = x on your graph you will see that the points of (y,x) are reflections of the points (x,y) about the line y = x.
here's your graph.
you find the reflected points about the line y = x by drawing a line vertical to that line (represented by y = -x) and then finding the intersection of that vertical line with the reflected lines of y = 5x and y = x/5.
the point of intersection will be interchanged.
(10,2) becomes (2,10) and (-10,-2) becomes (-2,-10) as seen on the graph.
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