Chapter 1: Q29RE (page 1)
Find the sum of the series.
The sum of the series is\({{\rm{e}}^{{\rm{( - e)}}}}\).
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Explain how each graph is obtained from the graph of\({\bf{y = f}}\left( {\bf{x}} \right)\).
(a)\({\bf{y = f}}\left( {\bf{x}} \right){\bf{ + 8}}\)
(b)\({\bf{y = f}}\left( {{\bf{x + 8}}} \right)\)\(\begin{array}{l}{\bf{y = f}}\left( {{\bf{x + 8}}} \right)\\{\bf{y = 8f}}\left( {\bf{x}} \right)\\{\bf{y = f}}\left( {{\bf{8x}}} \right)\\{\bf{y = - f}}\left( {\bf{x}} \right){\bf{ - 1}}\\{\bf{y = 8f}}\left( {\frac{{\bf{1}}}{{\bf{8}}}{\bf{x}}} \right)\\\end{array}\)
(c)\({\bf{y = 8f}}\left( {\bf{x}} \right)\)
(d)\({\bf{y = f}}\left( {{\bf{8x}}} \right)\)\(\)
(e)\({\bf{y = - f}}\left( {\bf{x}} \right){\bf{ - 1}}\)
(f)\({\bf{y = 8f}}\left( {\frac{{\bf{1}}}{{\bf{8}}}{\bf{x}}} \right)\)
Find
(a) \({\bf{f + g}}\)
(b) \({\bf{f}} - {\bf{g}}\)
(c) \({\bf{fg}}\)
(d) \({\bf{f}}/{\bf{g}}\)
and state their domains.
37. \({\bf{f}}\left( x \right) = {x^3} + 2{x^2}\) \(g\left( x \right) = 3{x^2} - 1\)
Find the functions (a) \({\bf{f}} \circ {\bf{g}}\) ,(b) \({\bf{g}} \circ {\bf{f}}\) ,(c) \({\bf{f}} \circ {\bf{f}}\) and (d) \({\bf{g}} \circ {\bf{g}}\) and their domains.
\({\bf{f}}\left( {\bf{x}} \right){\bf{ = x - 2}}\) \({\bf{g}}\left( {\bf{x}} \right){\bf{ = }}{{\bf{x}}^{\bf{2}}}{\bf{ + 3x + 4}}\)
Find the functions (a)\(f \circ g\), (b) \(g \circ f\),(c)\(f \circ f\), and (d) \(g \circ g\)
and their domains.
\(f\left( x \right) = \frac{x}{{1 + x}}\) \(g\left( x \right) = sin2x\)
Find\(fogoh\)
\(f\left( x \right) = \tan x\), \(g\left( x \right) = \frac{x}{{x - 1}}\), \(h\left( x \right) = \sqrt(3){x}\)
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