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f(x)=(2x+1)/(x-1) with domain x>3. (a)Find the inverse of f(x). (b)Find the range of f(x). (c) g(x)=x+5 for all x. Find the value of x such that fg(x)=3.

(a) Let y=f(x). Then y = (2x+1)/(x-1). Rearrange the equation to get x in terms of y to obtain the inverse function. This gives x=(1+y)/(y-2). So the inverse of f is f -1 (x)=(1+x)/(x-2) (b) Drawing a graph ...
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Answered by Lutfha A. • Maths tutor
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Solve this pair of simultaneous equations: 3x + 2y = 4 and 2x + y = 3

2x + y = 3 therefore y = 3 - 2x Substitute y = 3 - 2x in to the first equation: 3x + 2(3 - 2x) = 4 3x + 6 - 4x = 4 -x = -2 therefore x = 2 Substitute x = 2 in to either equation: 2(2) + y = 3 4 + y = 3 y = -1
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Answered by Tim C. • Maths tutor
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Solve x² - 3x - 2 = 0

To complete the square for the equation ax² + bx + c = 0 there are three steps.. 1. In order to complete the square, we need to take the first two parts of the quadtratic equation, and put them in the form o...
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Answered by Natalia M. • Maths tutor
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Use the equation 2(x+4) + 6(x-1) = 14, to find x.

Firstly, you need to get rid of any brackets. You do this by expanding them. This becomes 2x + 8 + 6x - 6 = 14. The next step is to get all the x's on one side, and all the numbers on the other. You already ...
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Answered by Ursula R. • Maths tutor
3736 Views

Find dy/dx for y = x^3*e^x*cos(x)

In this problem, we see that y is a product of 3 functions of x. That means that in order to find dy/dx we need to use the product rule. The product rule tells us that in this case we should differentiate on...
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Answered by Lyudmil N. • Maths tutor
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