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# P2 Functions Question watch

1. Help needed, i'll appreciate if someone can show me how to do this question NOV 2004 P2 Paper:

f:x --> Modulus 2x-5, X is set of Real Numbers

(b) Find the values of x for which f(x)=x (4 Marks)

The function g is defined by g: --> x(x-6), X is set of Real Numbers

(c) Find the range of g(x)

Many Thanx and Rep will be given!!!
2. (Original post by Steve8052)
Help needed, i'll appreciate if someone can show me how to do this question NOV 2004 P2 Paper:

f:x --> Modulus 2x-5, X is set of Real Numbers

(b) Find the values of x for which f(x)=x (4 Marks)

The function g is defined by g: --> x(x-6), X is set of Real Numbers

(c) Find the range of g(x)

Many Thanx and Rep will be given!!!
(b) f(x) = |2x - 5| = x
=> -x = 2x - 5 => x = 5/3
=> -x = -2x + 5 => x = 5

(c) g(x) = x^2 - 6x
g'(x) = 2x - 6 => x = 3 at minimum
g(3) = 9 - 18 = -9
Therefore g(x) > -9
3. b) Then x= |2x-5|
So x²=(2x-5)²=4x²-20x+25
So 3x²-20x+25=0
Solve quadratic:

x=(20±√(400-300))/6 = (20±10)/6
x either = 30/6=5 or 10/6=5/3

c) Expand the function to give x²-6x
Differentiatiate to give minima and maxima: 2x-6=0 x=3 is your minimum.

y=3*3 - 6*3 = 9-18=-9
g(x) is more than or equal to -9
4. Thanx Guys Help Appreciated!! Didnt know had to Differentiate that.

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