Chapter 3: Q4E (page 161)
Determine whether the function given by a table of values is one-to-one.
The resultant answer is a one-to-one function.
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(a) Determine the value of \({f^{ - 1}}(17)\) if\(f\) is one-to-one and \(f(6) = 17\).
(b) Determine the value of \(f(2)\) if\(f\) is one-to-one and \({f^{ - 1}}(3) = 2\).
(A) to determine the function\(f(x) = \frac{1}{{x - 1}},\;x > 1\)is one-to-one.\({f^{ - 1}}(x) = \frac{1}{x} + 1\)in
(B) To determine the value of\({\left( {{f^{ - 1}}} \right)^\prime }(2)\), where\(f(x) = \frac{1}{{x - 1}}\).
(C) To determine the inverse of the function\(f(x) = 9 - {x^2}\)and state its domain and range.
(D) To determine whether the value of\({\left( {{f^{ - 1}}} \right)^\prime }(2)\)is\(\frac{1}{4}\)using the inverse function.
(E) To sketch: The graph of\(f(x) = \frac{1}{{x - 1}}\)and\({f^{ - 1}}(x) = \frac{1}{x} + 1\)in the same coordinate.
Prove the identity\(sinh2x = 2sinhxcoshx\).
1–38 ■ Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.
11.\(\mathop {lim}\limits_{t \to 1} \frac{{{t^8} - 1}}{{{t^5} - 1}}\).
Determine the function \(f(x) = \frac{1}{{1 + a{e^{bx}}}},a > 0\) for various \(a\) and \(b\) values; explain how the graph change when the values of \(a\) and \(b\) are changed.
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