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Finding the Inverse of a Function (page 4 of 7) Sections: Definition / Inverting a graph, Is the inverse a function?, Finding inverses, Proving inverses
Since this passes the
Horizontal Line Test, you know that it's inverse will be a function.
And since this graph is different from that of the previous function,
you know that the inverse must be different. Again, it is very helpful
to first find the domains and ranges. The function's domain is
Then the inverse is y = sqrt(x – 1), x > 1, and the inverse is also a function.
Since the variable is in the denominator, this is a rational function. Here's the algebra:
This is just another rational function. The inverse function is y = (5x – 2) / x
The domain is
x >
2; the range (from
the graph) is y
< 0. Then
the domain of the inverse will be
Then the inverse y = x2 + 2 is a function, with domain x < 0 and range y > 2.
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