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Show that all automorphisms of a group G form a group under function composition.Then show that the inner automorphisms of G, defined by f : G--->G so thatf(x) = (a^(-1))(x)(a), form a normal subgroup of the group of all automorphisms.
For the first part, I can see that we need to show that f(g(x)) = g(f(x)) for x in G and use f(x)=x as the identity in the group, but I' not certain how to proceed to show all innG form a normal subgroup?
In 1990 the life expectancy of males in a certain country was 61.2 years. In 1996 it was 64.3 years. Let E represent the life expectancy in year t and let + represent the number of years since 1990.
Perform the computations and write your answer in scientific notation.
Use the following graph of a function f to determine x or y to the nearest integer as indicated. Some problems may have more than one answer.
Describe the transformation that transforms the curve y = √x to the curve y = √(x-4). The curve y = √x is stretched by a scale factor of 5 parallel to the x-axis. State the equation of the transformed curve.
What is the quadratic equation? Explain where the quadratic equation comes from. In particular, how is the quadratic equation related to the process of completing the square?
What must be true about the eigenvalues of the transition matrix if both populations die out in the long- run?
An interesting method for solving quadratic equations came from India. The steps are-Move the constant term to the right side of the equation. Multiply each term in the equation by four times the coefficient of the x2 term.
Which of the following points is a solution to this equation: y = -3x + 8
you must show your work on each of the following questions.rewrite y x2 14x 29 in general form.rewrite y 3x2 - 24x
Use S= C(1+r/100)^5 to find the inflated cost S, in 5 years, of an item, good or service, where C= (17,908.02 KRW) is the current price of that item in that country's currency
Write the slope intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of each equation:
The function, p(d)=1+(d/33), gives the pressure, in atmospheres (atm), at a depth d in the sea (d is in feet). Note that P(0)=1 atm, p(33)=2, and so on. Find the pressure at 50 feet.
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