Tracing the following proof, if q = 5/13 is given by the reader in line 1, what is the va f(x) = 5/13? You must enter your answer as a reduced fraction.

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
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Tracing the following proof, if q = 5/13 is given by the reader in line 1, what is the value of æ that makes
f(x) = 5/13? You must enter your answer as a reduced fraction.
3x +1
Claim. The function f:Q → Q with rule f(x) :
is onto.
2
Proof.
• Let q E Q be given.
2q – 1
• Set x =
3
2g
• f(x) = f(
and check:
(2g – 1) + 1
q.
|
3
2
• Since f(x)
= q and x E Q, this shows that f is onto.
Transcribed Image Text:Tracing the following proof, if q = 5/13 is given by the reader in line 1, what is the value of æ that makes f(x) = 5/13? You must enter your answer as a reduced fraction. 3x +1 Claim. The function f:Q → Q with rule f(x) : is onto. 2 Proof. • Let q E Q be given. 2q – 1 • Set x = 3 2g • f(x) = f( and check: (2g – 1) + 1 q. | 3 2 • Since f(x) = q and x E Q, this shows that f is onto.
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