SOLUTION: Consider the function defined by f(x)=sqrt(x-2)-1
a. use algebra to verify that the function is one-to-one.
b. sketch the graphs of f and f^-1 on the same coordinate axes. Labe
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Question 439741: Consider the function defined by f(x)=sqrt(x-2)-1
a. use algebra to verify that the function is one-to-one.
b. sketch the graphs of f and f^-1 on the same coordinate axes. Label each graph.
This area of PreCal is foreign to me and I am in need of help. I would appreciate any help I receive. Thank you.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Some functions do not have inverses. If a function never takes on the same value twice, then it has inverse. You can tell if a function has an inverse by drawing a horizontal line across its graph. If no horizontal line intersects its graph more than once then it has a one to one relationship and has and inverse.
In the graphs below the top ((x+2)^2-1) fails the horizontal line test and does not have an inverse. The bottom ((x+2)^3-1) has an inverse because it passes the horizontal line test. For every value of x there is only one value of y. It is one to one.
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Ed
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