(1) Define the function f : RR by f(x) at a = 1. 2-x x < 1 x1 Show that f is continuous
(1) Define the function f : RR by f(x) at a = 1. 2-x x < 1 x1 Show that f is continuous
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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Definition 6.1.1. Given D ⊆ R, a function f : D → R and some point a ∈ D, then f is continuous at a if for all sequences (Xn) contained in D where lim Xn =
n→∞
a, we have that lim f(Xn) = f(a) (that is, the sequence f(Xn) is difined by taking
n→∞
for each n-th term the image of xn under f converges to the value f(a)).
A function is continuous on its domain if it is continuous at a for all a ∈ D.please use this definition to solve the problem
Transcribed Image Text:(1) Define the function f : R→ R by f(x)
at a = 1.
2 - x
{2-
x2
x<1
x ≥1\
•
Show that f is continuous
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