Show that the function (f : [0, infinity) -> R given by f(x) = e^{2x} - 2e^x + 2 ] has an inverse function. Also, find the expression and domain of the inverse function.
Show that the function (f : [0, infinity) -> R given by f(x) = e^{2x} - 2e^x + 2 ] has an inverse function. Also, find the expression and domain of the inverse function.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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a) Show that the function (f : [0, infinity) -> R given by f(x) = e^{2x} - 2e^x + 2 ] has an inverse function. Also, find the expression and domain of the inverse function.
b) Which of the four functions (f : D(f) -> R )(1)-(4) from the image, with the specified domains (D(f)), have an inverse function? Justify why.
c) For the cases in (b) where (f) has an inverse function, find the domain and range of the inverse function.
Transcribed Image Text:2
(1) f(t)=rtan(;), D(f)=(−1,1);
(2) f(2)=rtan(2), D(f)=[0, 1);
(3) f(x) = 3x²-1, D(ƒ) = (−∞, 0) U (0, ∞);
1,
x rasjonal;
(4) f(x) =
=
D(f) = R.
0,
x irrasjonal,
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