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g(x) = x/(x+3) + 3(2x+1)/(x^2 +x - 6) a)Show that g(x) =(x+1)/(x-2), x>3 b)Find the range of g c)Find the exact value of a for which g(a)=g^(-1)(a).

a) First, we need to factorize (x 2 +x-6) = (x-2)(x+3). Therefore, g(x) = x/(x+3) + 3(2x+1)/(x-2)(x+3) = x(x-2)/(x-2)(x+3) + 3(2x+1)/(x-2)(x+3) = (x 2 -2x + 6x +3)/(x-2)(x+3) = (x 2 +4x+3)/(x-2)(x+3).Now we ...
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Answered by Teodora M. • Maths tutor
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Find the integral of ((2(7x^(2)-xe^(-2x))-5)/x) . Given that y=27 at x=1, solve the differential equation dy/dx=((2(7x^(2)-xe^(-2x))-5)/-3x).y^(2/3) in terms of y.

Part A)Expand numerator in the integral to get 14x^(2) - 2xe^(-2x)-5Now divide by denominator to get 14x - 2e^(-2x) - 5/xNow integrate to get 7x^(2) + e^(-2x) - 5ln(x)Part B)Get all components of y on the le...
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Answered by George R. • Maths tutor
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x + y = 11, and x^2 + y^2 = 61, Work out values of y in the form of x

This is a simultaneous equation question, and it is important to read the question and pick out the information we want, and see what we are trying to get to, then work out a pathway on how we will get to it...
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Answered by Venkat V. • Maths tutor
5139 Views

What do I include in a Medicine Personal statement?

It is hard to write a personal statement, it's not something that's hardwired into our system since we were little, then suddenly you are here trying to apply for jobs, sixth form, and university, which all ...
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2627 Views

How can I revise for the Abstract Reasoning subset of the UKCAT?

There are many ways to tackle AR subset. My top tips would be to use Medify, Medic Portal, and the ISC Medical book for practise and I will also guide you through examples to explain in greater depth each qu...
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Answered by Venkat V. • UCAT tutor
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