Question

3. The functions f and g are defined by f: x → ax – b where a and b are constants and g: x → X+4.

Given fg(2) = 9 and gf (1/2) = 2, find the value of a and of b. ​

hiii this is adddmath can anyone help with this please

Answer 1

fg(2) = 9 means that f(g(2)) = 9

We know that g(2) = 6

So f(6) = 9 which means that

6a - b = 9 (note 1)

And we know that g(f(1/2)) = 2

And we know that f(1/2) = 1/2(a) - b

So g(1/2(a) - b) = 2

Meaning that 1/2(a) - b + 4 = 2

So 1/2(a) - b = - 2 (note 2)

Using note 1 and 2 we can solve the equation

11/2(a) = 11 so a = 2 and b = 3