No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.
No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.
No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.
No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.
A monotonic, or one-to-one function.
XX or X*X, can be written as X squared. The inverse of a function "sort of cancels it out". I know the inverse of a square is the square root. Since we need the inverse of X squared, it's inverse is the square root of X. sqrt(x)
That's related to the fact that, for example, x squared is the same as (-x) squared. Note that any equation of the form "x squared + bx + c = 0", with constants a, b, and c can be rewritten as "(x - d) squared + f = 0", for possibly different constants d and f.
(X2) (X2) = X4 x squared multiplied by x squared is x raised to the 4th power.
To shift a funcion (or its graph) down "a" units, you subtract "a" from the function. For example, x squared gives you a certain graph; "x squared minus a" will give you the same graph, but shifted down "a" units. Similarly, you can shift a graph upwards "a" units, by adding "a" to the function.
X squared is not an inverse function; it is a quadratic function.
No. For example, y = 7 is monotonic. It may be a degenerate case, but that does not disallow it. It is not a bijection unless the domain and range are sets with cardinality 1. Even a function that is strictly monotonic need not be a bijection. For example, y = sqrt(x) is strictly monotonic [increasing] for all non-negative x. But it is not a bijection from the set of real numbers to the set of real numbers because it is not defined for negative x.
They can be either, but not together. y = x and y = -x are both monotonic.
Answer: As for example the square root of 16 is -4 or +4 because -4 times -4 = 16 and 4 times 4 = 16 Answer: There are two "answers", because there are two numbers which, when squared, give you a specified number. The reason for this is that the square function is not monotonic - this results in complications when determining the inverse function. For more details, read about "monotonic function", for example in the Wikipedia.
A monotonic, or one-to-one function.
No, they can only be jump continuous.
Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
XX or X*X, can be written as X squared. The inverse of a function "sort of cancels it out". I know the inverse of a square is the square root. Since we need the inverse of X squared, it's inverse is the square root of X. sqrt(x)
Answer: The difference between the square root of x and squared is either x or -x. Answer: The square root is the inverse function of the square function. That means that it's basically the opposite. Asking for the square root of "x" is like asking "what number must I square to get 'x'".
8
That's related to the fact that, for example, x squared is the same as (-x) squared. Note that any equation of the form "x squared + bx + c = 0", with constants a, b, and c can be rewritten as "(x - d) squared + f = 0", for possibly different constants d and f.
square root of x/pi