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Unformatted text preview: Section 1.6 Number 53
www.math.uﬂ.edu/˜harringt
January 24, 2008
We want to Find the range of f (x) =
know that that f −1 (x) = 1 ln(3 − x2 ).
2 √ 3 − e2x . From the quiz 3A we Recall that the range of f (x) is the domain of f −1 (x). Since we need to
know the domain of f −1 (x) = 1 ln(3 − x2 ), then we must have that 3 − x2 > 0
2
3 − x2
3
√
3
√
3
x >
>
>
>
< 0
x2
√
x2
x
√
3 √
√
So − 3 <√ < 3. WAIT, there is more! We should also notice that
x
since f (x) = 3 − e2x , then f (x) cannot be negative. Recall that square
roots can not produce negative numbers. So the range of f must be
√
0 ≤ f (x) < 3
or in interval notation
[0, √ . 1 3) ...
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This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Math, Calculus, Geometry

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