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Is a monotonic function a bijection?
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.
Explain why a and b must be equal if log a equals log b?
It is because the logarithm function is strictly monotonic.
Is every bijection a strictly monotonic function?
No. For example, consider the discontinuous bijection that increases linearly from [0,0] to [1,1], decreases linearly from (1,2) to (2,1), increases linearly from [2,2] to [3,3], decreases linearly from (3,4) to (4,3), etc.
Is 18 a square number why or why not?
It is a square number but not a perfect square. The nearest perfect squares, on either side, are 4^2 = 16 and 5^2 = 25. Since there is no integer between 4 and 5 and the square is a strictly monotonic function, 18 cannot be a perfect square.
How do you use strictly in a sentence?
I Stictly told you not to do that. (strictly- strongly recommended)
Is a monotonic function a bijection?
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.
Explain why a and b must be equal if log a equals log b?
It is because the logarithm function is strictly monotonic.
Is every bijection a strictly monotonic function?
No. For example, consider the discontinuous bijection that increases linearly from [0,0] to [1,1], decreases linearly from (1,2) to (2,1), increases linearly from [2,2] to [3,3], decreases linearly from (3,4) to (4,3), etc.
Is 18 a square number why or why not?
It is a square number but not a perfect square. The nearest perfect squares, on either side, are 4^2 = 16 and 5^2 = 25. Since there is no integer between 4 and 5 and the square is a strictly monotonic function, 18 cannot be a perfect square.
What are similarities between linear and exponential functions?
neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve
Can you feed a green iguana crickets?
Absolutely not! Iguanas are strictly herbivores.
Is metalica a bluegrass band?
absolutely not. purely and strictly heavy metal.
What is currently the UK's longest continuous running game show?
Strictly come dancing
What are the characteristics of graph of exponential function?
If graphed in standard form (for example, x-axis is horizontal, with increasing values towards the right):The function value increases from left to right (it is strictly increasing monotonic).The function is concave upwards (its slope increases from left to right).It crosses the y-axis a y = 1.Values are always positive.Towards the left, values get closer and closer to zero, but never quite reach it (if x tends towards minus infinity, y tends towards zero).Towards the right, the function value is unbounded (if x tends towards plus infinity, y tends towards plus infinity).
Under normal circimstances officers and enlisted can share living accommodations?
Absolutely not. That's considered fraternization, and is very strictly prohibited.
How do you show log x is convex?
Log x is defined only for x > 0. The first derivative of log x is 1/x, which, for x > 0 is also > 0 The second derivative of log x = -1/x2 is always negative over the valid domain for x. Together, these derivatives show that log x is a strictly monotonic increasing function of x and that its rate of increase is always decreasing. Consequently log x is convex.
Can someone say sorry to WikiAnswers if they have done cyberbullying?
Absolutely. However, this won't get you back on the site. Cyberbulling is strictly prohibited and there is no tolerance for it on this site.
