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Consider f:R -> R, f = x/ sqrt(x^2+1). Prove that for any a between -1 and 1, f(x)=a has only one solution.

f'(x)=( sqrt (x^2+1) - x * ( x / sqrt (x^2 +1) ) ) / (x^2+1) = (x^2 + 1 + x^2) / ( (x^2 + 1) * sqrt ( x^2 + 1) ) = 1 / ( (x^2 + 1) * sqrt (x^2 + 1) ). f'(x) > 0 for any x => f is increasing. When x-&gt...
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How would sociologists define crime?

A simple definition of crime would be that a criminal behaviour is a behaviour that is breaking the law. However, crime is a much more complex concept to define. To extend the previous simple definition, cri...
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Answered by Carina K. • Sociology tutor
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What is the point of intersection of two lines, and how would I find it?

The point of intersection is where the lines would cross if we drew them on the same graph, in your exam you may be asked to find the coordinates of this point. To do this we would first draw a sketch of the...
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Answered by Lisa S. • Maths tutor
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factorise x^2+5x+6=0 and find x

x 2 +5x+6=0 (x+3)(x+2)=0 x=-3 and x=-2
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Answered by Ashley O. • Maths tutor
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Solve 7x - 3 = 4x + 6

To solve the equation first collect all the unkown terms (letters) on one side and the known terms (numbers) on the other. Remember you must do the same to both sides to keep it balanced. First remove the 4x...
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Answered by Emily H. • Maths tutor
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