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f:x-->2x^2+1 and g:x--> 2x/(x-1) where x is not equal to 1. express the composite function gf as simply as possible

need to put f equation into g equation so replace x in g equation with 2x^2+1 gf : x --> 2(2x^2+1) / ((2x^2+1)-1) then need to simplify (expand brackets) 4x^2 + 2 / 2x^2 divide all by 2 (common factor) gf...
EI
Answered by Elysa I. • Maths tutor
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Factorise 3y^2 + 2y

Factorise = take out common term (y in this case) so divide each by y i.e. 3y^2 / y = 3y 2y / y = 2 thus factorised: = y(3y+2)
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Answered by Elysa I. • Maths tutor
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Jamil has 5 litres of water in a container. He pours 750 millilitres of water into each of 6 bottles. (c) How much water is left in the container? Give your answer in millilitres.

5L water = 5000mL because 1L = 1000mL so multiply by 5 if 750mL is poured into 6 bottles, first need to see how much total has been poured. therefore, do 750mL * 6 = 4500mL so original = 5000mL minus what po...
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Answered by Elysa I. • Maths tutor
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Use the geometric series formula to find the 9th term in this progression : 12 18 27...

Formula for nth term in a geometric progression = ar^n-1 workings: a=12 r=1.5 because 18/12 = 1.5 Thus, using ar^n-1 --> 12 * 1.5^8 = 307.54... or 308 (to 3sf) (In an ideal scenario question we'd be worki...
PF
Answered by Philip F. • Maths tutor
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A tank contains 45 000 cm3 of water. The tank leaks at 0.75 litres/minute. How long does the tank take to empty?

The first thing to notice with this question is that the volume of the tank is given in cm 3 yet the rate at which the water leaks is in litres, so a conversion of units will be neccessary. We know that ther...
TG
Answered by Tom G. • Maths tutor
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