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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
4672 Views

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
5215 Views

1 a. If x=6a+3 and a is 4 what is x? b. Make a the subject of the formula.

1a. a=4 Substitute the number into the equation x= (6 x 4) + 3= 24 + 3= 27 b. We need to isolate a So minus three from both sides to start with (what you do to one side you must do to the other, otherwise yo...
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Answered by Emma W. • Maths tutor
3529 Views

If a cookie recipe requires 280g of flour for 12 cookies how much flour is needed to make only 9 cookies

9/12 = 3/43/4 * 280 = (3 * 280) / 4 = 3 * 70 = 210so only 210 g is needed for 9 cookies.
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Answered by Ben W. • Maths tutor
4602 Views