1.) Simplify the following: (a) (ln 2 + ln 3)/ ln 36 (b) e^−2 ln x (c) ln(e(^−x^2)) 2. Let f(x) = mx + b, where m≠ 0. Show that f has an inverse, and find a formula for f ^−1. Finally,explain why f does not have an inverse if m = 0. 3. (a) Suppose that the formula y = f(x) defines a function f that has an inverse on [a, b]. Describe the 2 steps you would use in order to find a formula for the inverse f^−1. (b) Let f(x) = 3/x. Draw the graph of f , then find a formula for f ^−1, and conclude that f ^−1 = f. Do the same for g(x) = −3/x. (c) What property of the graph of a function h implies that h^−1 = h?
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
1.) Simplify the following: (a) (ln 2 + ln 3)/ ln 36
(b) e^−2 ln x
(c) ln(e(^−x^2))
2. Let f(x) = mx + b, where m≠ 0. Show that f has an inverse, and find a formula for f ^−1. Finally,explain why f does not have an inverse if m = 0.
3. (a) Suppose that the formula y = f(x) defines a function f that has an inverse on [a, b]. Describe the 2 steps you would use in order to find a formula for the inverse f^−1.
(b) Let f(x) = 3/x. Draw the graph of f , then find a formula for f ^−1, and conclude that f ^−1 = f. Do the same for g(x) = −3/x.
(c) What property of the graph of a function h implies that h^−1 = h?
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