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1. 2. Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x². (a) Calculate (go f)(2). (b) Find an explicit formula for the function gof. Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1. Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.

1. 2. Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x². (a) Calculate (go f)(2). (b) Find an explicit formula for the function gof. Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1. Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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1. 2. Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x². (a) Calculate (go f)(2). (b) Find an explicit formula for the function gof. Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1. Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.
Transcribed Image Text:1. 2. Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x². (a) Calculate (go f)(2). (b) Find an explicit formula for the function gof. Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1. Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.
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