Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
The function f-1 is an inverse function of f if f(ƒ −¹(x)) = ƒ−¹(f(x)).
To verify, consider f(x) = 5x – 8 and ƒ −¹(x)
f(f−¹(x)) = f−¹(f(x))
f(f-1(x)) = f (x + 8)
5
Hence,
= 5(x + 8).
5
= x + 8 - 8
=
ƒ−¹(f(x)) = f−¹(
||
(5x
-
8
8) + 8
5
f(f−¹(x)) = f−¹(f(x))
So the domain of f inverse is not
=
X + 8
5
- 8)
the range of f.
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Transcribed Image Text:The function f-1 is an inverse function of f if f(ƒ −¹(x)) = ƒ−¹(f(x)). To verify, consider f(x) = 5x – 8 and ƒ −¹(x) f(f−¹(x)) = f−¹(f(x)) f(f-1(x)) = f (x + 8) 5 Hence, = 5(x + 8). 5 = x + 8 - 8 = ƒ−¹(f(x)) = f−¹( || (5x - 8 8) + 8 5 f(f−¹(x)) = f−¹(f(x)) So the domain of f inverse is not = X + 8 5 - 8) the range of f.
Expert Solution
Check Mark
Step 1: Given Function And Inverse Functions

given f(x)=5x-8 and f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 8 over denominator 5 end fraction

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