Question 1. a) Find the asymptotes of the function f(x): = 5x 2x²-2 and sketch its graph. Also determine the domain and range of the given function. 2x+3 b) Given f(x)= and g(x) = x, show that f(x) and g(x) are inverse functions. 5 1 c) Restrict the domain of the function f(x) = so that it will have an inverse. Hence find its inverse.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 1.
a) Find the asymptotes of the function f(x)
and range of the given function.
2x+3
5
c) Restrict the domain of the function f(x) =
so that it will have an inverse. Hence find its inverse.
3x²
b) Given f(x)
=
5x
2x²-2
=
and sketch its graph. Also determine the domain
5
3
and g(x) = ²x - 2²/1 show that f(x) and g(x) are inverse functions.
2'
Transcribed Image Text:Question 1. a) Find the asymptotes of the function f(x) and range of the given function. 2x+3 5 c) Restrict the domain of the function f(x) = so that it will have an inverse. Hence find its inverse. 3x² b) Given f(x) = 5x 2x²-2 = and sketch its graph. Also determine the domain 5 3 and g(x) = ²x - 2²/1 show that f(x) and g(x) are inverse functions. 2'
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