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If f:[3,00) →R, f(x) = x² +k and g:[2,00)→R, g(x) =-+k, where k is a positive constant, find the value(s) of k such that both f(g(x)) and g(f(x)) are defined.

If f:[3,00) →R, f(x) = x² +k and g:[2,00)→R, g(x) =-+k, where k is a positive constant, find the value(s) of k such that both f(g(x)) and g(f(x)) are defined.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Revision 1. 1 If f:[3,0) →R, f(x) =x²+k and g:[2,00)→R, g(x)=-+k, where k is a a positive constant, find the value(s) of k such that both f(g(x)) and g(f(x)) are defined. a 0Tx The transformation T:R² → R² is defined by T b where a, b, c and d are non-zero real numbers. If the image of the curve g(x) = -2x-2+2 is f(x) =x, find the values of a, b, c and d.
Transcribed Image Text:Revision 1. 1 If f:[3,0) →R, f(x) =x²+k and g:[2,00)→R, g(x)=-+k, where k is a a positive constant, find the value(s) of k such that both f(g(x)) and g(f(x)) are defined. a 0Tx The transformation T:R² → R² is defined by T b where a, b, c and d are non-zero real numbers. If the image of the curve g(x) = -2x-2+2 is f(x) =x, find the values of a, b, c and d.
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