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The functions f and g are such that f(x)=5x+2 and g(x)=-x-4. a) Find fg(x). b) Find ff(x). c) Solve fg(x) = ff(x).

a) fg(X) = 5(-x-4)+2 = -5x-20+2 = -5x-18b) ff(X) = 5(5x+2)+2 = 25x+10+2 =25x+12c) 25x+12=-5x-18 25x+5x=-18-12 30x=-30 x=-1
MA
Answered by Maria A. • Maths tutor
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Differentiate sin^2(x)

sin(2x)
JP
Answered by James P. • Maths tutor
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Find g(f(x)) where g(x)=2x+4 and f(x)=x^2+1.

With functions of functions you work from the inside out, so you substitute the function f(x) for the x in g(x). We know that f(x)=x 2 +1 and g(x)=2x+4. In this question you therefore replace the x in 2x+4 w...
GM
Answered by Georgina M. • Maths tutor
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Factorise 3x^2 + 14x + 8

To factorise polynomials of the form a x^2 + b x + c , we want to rewrite the middle coefficient as the sum of two smaller numbers. The product of these two numbers should be equal to a * c (in this case, 3 ...
AM
Answered by Alex M. • Maths tutor
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A circle C1 has a centre at (3,0) and a radius 8. A second circle C2 has a centre (x,0) and radius 6. Given the radii of the 2 circles meet at right angles. Find x

Gven the radii of the circles meet at right angles then a right angled triangle can be constructed were the hypotenuse is the distance between the centres. Using the Pythagorean triplet, the hypotenuse is 10...
AJ
Answered by Adam J. • Maths tutor
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