3. Let l be a line and assume that f :l→R is a coordinate function for e.a. Let -f:(→R be defined by (-f)(P) = -f(P) for every PE l. Prove that -fis also a coordinate function for l.b. Let c be a constant and let g: e R be defined by g(P) = f(P) + e for everyPE l. Prove that g is also a coordinate function for .%3D

Given that f:l→ℝ is a coordinate function for l. To prove (a) and (b):

3. Let ( be a line and assume that f:lR is a coordinate function for (. a. Let -f:(R be defined by (-)(P) = -f(P) for every PE l. Prove that -f is also a coordinate function for . b. Let e be a constant and let g: lR be defined by g(P) = f(P) + c for every PEl. Prove that g is also a coordinate function for .

3. Let ( be a line and assume that f:lR is a coordinate function for (. a. Let -f:(R be defined by (-)(P) = -f(P) for every PE l. Prove that -f is also a coordinate function for . b. Let e be a constant and let g: lR be defined by g(P) = f(P) + c for every PEl. Prove that g is also a coordinate function for .

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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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.

Question

3. Let l be a line and assume that f :l→R is a coordinate function for e.
a. Let -f:(→R be defined by (-f)(P) = -f(P) for every PE l. Prove that -f
is also a coordinate function for l.
b. Let c be a constant and let g: e R be defined by g(P) = f(P) + e for every
PE l. Prove that g is also a coordinate function for .
%3D

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