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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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since the point A is located on both graphs, then its coordinates verify the equations of the functions f and g.

f(2) = 3

f(2) = 2a + b - 9

2a + b - 9 = 3

We'll move the numbers alone to the right side, keeping a and b to the left side:

2a + b = 12 (1)

Also, g(2) = 3

g(2) = 4b - a

-a + 4b = 3 (2)

We'll mutliply (2) by 2:

-2a + 8b = 6 (3)

We'll add (3) to (1):

2a + b - 2a + 8b = 12 + 6

We'll eliminate like terms:

9b = 18

b = 2

a = 4b - 3

a = 8 - 3

a = 5

The values of a and b are: a = 5 and b = 2.

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