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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 (x2+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) = (x2-2x + 6x +3)/(x-2)(x+3) = (x2<...

TM
Answered by Teodora M. Maths tutor
16124 Views

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...

GR
Answered by George R. Maths tutor
4194 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...

VV
Answered by Venkat V. Maths tutor
4374 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, oth...

EW
Answered by Emma W. Maths tutor
2965 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.

BW
Answered by Ben W. Maths tutor
3964 Views

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