2) Consider the functions: f(x) = 3x + 1; g(x) = ². Additionally, let h(x) = which has a horizontal asymptote at y = 0. a) What is f-¹(x)? 6 b) show that (go f-¹)(x) = x₁ c) Find the y-intercept of h(x). d) i) Find the x-intercept of h-¹(x). ii) What is the equation for the vertical asymptote of h-1(x). e) If h-¹(c) = 4, find the value of c.

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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2) Consider the functions: f (x) = 3x + 1; g(x) = ². Additionally, let h(x) = ₁, which has a horizontal
x-1'
asymptote at y = 0.
a) What is f-¹(x)?
6
b) show that (go f-¹)(x) = x-1
c) Find the y-intercept of h(x).
d)
i) Find the x-intercept of h-¹(x).
ii) What is the equation for the vertical asymptote of h-¹(x).
e) If h-¹(c) = 4, find the value of c.
Transcribed Image Text:6 2) Consider the functions: f (x) = 3x + 1; g(x) = ². Additionally, let h(x) = ₁, which has a horizontal x-1' asymptote at y = 0. a) What is f-¹(x)? 6 b) show that (go f-¹)(x) = x-1 c) Find the y-intercept of h(x). d) i) Find the x-intercept of h-¹(x). ii) What is the equation for the vertical asymptote of h-¹(x). e) If h-¹(c) = 4, find the value of c.
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