2.3 Consider the following two functions: g(t) = (g1(t), 92(t)) = (1 +t, 3 – 2t) (7) %3D f(x) = = +1 (8) %3D 2.3.1 For each of the two functions, draw the image of the function and state the domain and target space of the function. Explain whether the functions are onto or not? ' 2.3.2 Now consider the case where f(x) = t. Derive a third function h(x), which %3D is the composition of functions (7) and (8), as in h(x) = g(f (x)).
2.3 Consider the following two functions: g(t) = (g1(t), 92(t)) = (1 +t, 3 – 2t) (7) %3D f(x) = = +1 (8) %3D 2.3.1 For each of the two functions, draw the image of the function and state the domain and target space of the function. Explain whether the functions are onto or not? ' 2.3.2 Now consider the case where f(x) = t. Derive a third function h(x), which %3D is the composition of functions (7) and (8), as in h(x) = g(f (x)).
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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Transcribed Image Text:2.3 Consider the following two functions:
g(t) = (g1(t), g2(t)) = (1 +t, 3 – 2t)
(7)
1
f(x)
= - + 1
(8)
2.3.1 For each of the two functions, draw the image of the function and state the
domain and target space of the function. Explain whether the functions are
onto or not?
2.3.2 Now consider the case where f(x) =t. Derive a third function h(x), which
is the composition of functions (7) and (8), as in h(x) = g(f(x)).
2.3.3 Using the chain rule and without using substitution, derive an equation for
dh
dr
, using functions (7) and (8).
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