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Question 126702: Hey again..
I'm working on the section inverse relations and functions and have a question. Heres the problem.
Find the inverse of the function y=4x-7. Is the inverse a function?
I found the inverse... its y=x+7/4 I just dont know if its a function or not?
Thank you for helping
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the inverse of the function y=4x-7. Is the inverse a function?
I found the inverse... its y=(x+7)/4 I just dont know if its a function or not?
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Your inverse equation can be written in the form y = (1/4)x +(7/4),
which is the form of a line. It is a function because for any value
you would give "x", there would be only one "y" value.
====================
Cheers,
Stan H.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Check your answer again.
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You are given the function:
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y = 4x - 7
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To find the inverse of this, replace y with x and x with y to get:
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x = 4y - 7
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Solve this for y. Begin by transposing the equation (just swapping sides to get the term
containing y on the left side). After transposing, the equation is:
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4y - 7 = x
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Get rid of the -7 on the left side by adding 7 to both sides to get:
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4y = x + 7
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Then solve for y by dividing both sides of this equation by 4 to get:
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y = (1/4)x + 7/4
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This is the inverse of the function y = 4x - 7.
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That may have been the answer you got. If so you should have written it as:
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y = (x + 7)/4
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so that it was clear that both terms, the x and the 7, were to be divided by 4. According to
the rules of algebra, the way you wrote the answer, only the 7 was divided by 4 and x was then
added to the result of that division so that the answer was x + (7/4).
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Now, how do you tell whether or not that the inverse is a function? Look at the answer:
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y = (1/4)x + (7/4)
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This is in the form of a slope intercept equation ... the slope is (1/4) and the y-intercept
is at +7/4 on the y-axis. The graph is a straight line. ... And the graph looks like this:
.
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One way to tell if this is a function is if you can draw a vertical line anywhere on
the graph and it only intersects the graphed line at a maximum of one point, the graphed line
represents a function. On the graph shown above, anywhere you draw a vertical line it will cross the
graphed line only at one point, so you have a function. If somewhere on the graph a
vertical line could cross the graphed line at more than one point, then the graph would
not represent a function.
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So the answer to your problem is yes ... the inverse is a function.
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Hope this helps you to understand one way of determining whether an expression represents
a function.
.
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