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What is the derivative of x times root x?
x*x1/2= x3/2 Derivative = 3/2 * x1/2
Why does line parallel to the x-axis will intersect the graph of a function once at most if the function has an inverse?
Suppose you have a function y = f(x) which has an inverse. Therefore there exists a function g(y) such that g(y) = x whenever y = f(x). Now suppose a line parallel to the x axis, y = k (some constant), intersects the graph of y = f(x) at more than one point: say x1 and x2. That means that k = f(x1) and k = f(x2). Now, in the context of the function g, this means that [from the first intersection] g(k) = x1 and [from the first intersection] g(k) = x2 But the function g cannot map k to two different points. That is the contradiction which precludes the possibility of a horizontal line intersecting an invertible function more than once.
Describe in detail the types of functions and the transformation of the function f(x) = - 2|x + 8| - 5 from its parent function g(x) = |x?
44=2
What is the fourth root of x to the fourth power?
It is x1 which is x.
How are fractional exponents and radicals are related?
Here are some examples. x1/2 = square root of x; x1/3 = cubic root of x; in general, x1/n = nth root of x. Also, x2/3 = the square of the cubic root of x, or equivalently, the cubic root of the square of x.
