The function f-1 is an inverse function of ƒ if f(ƒ −¹(x)) = f−¹(f(x)). To verify, consider f(x) = 5x f(f−¹(x)) = f−¹(f(x)) f(F-¹(x)) = f (X + 8) 5 Hence, = 5(x + 8) - = x + 8 - 8 || 8 and f-¹(x): ƒ−¹(f(x)) = f−¹( || f(ƒ −¹(x)) = ƒ −¹(f(x)) 8 (5x – 8) + 8 5 = X + 8 5 - 8)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.
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
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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