Chapter 1: Q23E (page 9)
Evaluate the difference quotient for the given function. Simplify your answer.
\(f\left( x \right) = \frac{1}{x}\), \(\frac{{f\left( x \right) - f\left( a \right)}}{{x - a}}\)
The value of the expression \(\frac{{f\left( x \right) - f\left( a \right)}}{{x - a}}\)is\( - \frac{1}{{ax}}\).
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Find the functions (a)\({\bf{f}} \circ {\bf{g}}\), (b)\({\bf{g}} \circ {\bf{f}}\), (c)\({\bf{f}} \circ {\bf{f}}\), (d) \({\bf{g}} \circ {\bf{g}}\) and their domains.
\({\bf{f}}\left( {\bf{x}} \right){\bf{ = 1 - 3x}}\) \({\bf{g}}\left( {\bf{x}} \right){\bf{ = cosx}}\)
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
\(y = \frac{2}{{x + 1}}\)
Prove the statement using the\(\varepsilon \) \(\delta \)definition of a limit.
\(\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} + x - 6}}{{x - 2}} = 5\)
Determine whether is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually.
\({\bf{f}}\left( {\bf{x}} \right){\bf{ = x}}\left| {\bf{x}} \right|\)
Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.
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