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#further-maths
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The function f and g on the set of real number are defined by f(x)=2x-7
g(x) = x-4/2x+1;[x= - 1/2]
Find (a) gof (x). (b) fog(x)?

Feb 23

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Feb 23

(a) To find gof(x), we first need to find g(f(x)):

g(f(x)) = g(2x-7)

Now, substitute 2x-7 into g(x):

g(2x-7) = (2x-7 - 4) / (2(2x-7) + 1)

= (2x-11) / (4x-14 + 1)

= (2x-11) / (4x-13)

Therefore, gof(x) = (2x-11) / (4x-13)

(b) To find fog(x), we need to find f(g(x)):

f(g(x)) = f(x-4/2x+1)

Now, substitute x-4/2x+1 into f(x):

f(x-4/2x+1) = 2(x-4/2x+1) - 7

= 2x - 8/2x + 2 - 7

= 2x - 4x + 2 - 7

= -2x - 5

Therefore, fog(x) = -2x - 5

g(f(x)) = g(2x-7)

Now, substitute 2x-7 into g(x):

g(2x-7) = (2x-7 - 4) / (2(2x-7) + 1)

= (2x-11) / (4x-14 + 1)

= (2x-11) / (4x-13)

Therefore, gof(x) = (2x-11) / (4x-13)

(b) To find fog(x), we need to find f(g(x)):

f(g(x)) = f(x-4/2x+1)

Now, substitute x-4/2x+1 into f(x):

f(x-4/2x+1) = 2(x-4/2x+1) - 7

= 2x - 8/2x + 2 - 7

= 2x - 4x + 2 - 7

= -2x - 5

Therefore, fog(x) = -2x - 5