Given the functions f(x)=ax+b-9 and g(x)=2bx-a find a and b if the point A(2,3) is on the graphs of f and g.

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The point (2 , 3) lies on the graph f(x) and g(x).

So we have 3 = a*2 + b - 9

and 3 = 2*b*2 - a

This gives us two equations to solve for a and b.

2a + b = 12...(1)

4b - a = 3 ...(2)

...

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The point (2 , 3) lies on the graph f(x) and g(x).

So we have 3 = a*2 + b - 9

and 3 = 2*b*2 - a

This gives us two equations to solve for a and b.

2a + b = 12...(1)

4b - a = 3 ...(2)

4b - a = 3

=> a = 4b - 3

substitute in (1)

2(4b - 3) + b = 12

=> 8b - 6 + b = 12

=> 9b = 18

=> b = 2

a = 4*2 - 3 = 5

The required values are a = 5 and b = 2

 

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