8. (a) Determine whether the mapping f: QQ defined by ƒ() = ² Vm,n EZ, n #0 n is well defined function. Justify your answer. (b) Let f (R\{1}) → (R\ {1}) be a function defined by X f(x)=xVxER\ {1}. Find f and verify that it is indeed an inverse function for the function f. (c) Determine whether or not the functions f: R→ R defined as follows x f(x) = x² +1' is one-to-one.
8. (a) Determine whether the mapping f: QQ defined by ƒ() = ² Vm,n EZ, n #0 n is well defined function. Justify your answer. (b) Let f (R\{1}) → (R\ {1}) be a function defined by X f(x)=xVxER\ {1}. Find f and verify that it is indeed an inverse function for the function f. (c) Determine whether or not the functions f: R→ R defined as follows x f(x) = x² +1' is one-to-one.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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Transcribed Image Text:8. (a) Determine whether the mapping f: QQ defined by
²
is well defined function. Justify your answer.
Vm, n E Z, n # 0
(b) Let f: (R\{1}) → (R\ {1}) be a function defined by
f(x)=₁, Vx € R\{1}.
x-1'
Find f1 and verify that it is indeed an inverse function for the function f.
is one-to-one.
(c) Determine whether or not the functions f:R→ R defined as follows
f(x) =
x² + 1
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