F(x) = ax + b and g (x)= x-4,where a and b are constant .if fg (4) = 2 and gf(2)=4,find the values of a and b.

 a = 3, b = 2

Step-by-step explanation:

f(x) = ax + b          f(2) = 2a + b

g(x) = x - 4            g(4) = 4 - 4   ⇒  g(4) = 0

f(g(4)) = 2   ⇒   f(0) = 2

and f(0) = a(0) + b   ⇒   f(0) = b

                                      ⇒    2 = b

g(f(2)) = 4     ⇒    g(2a+b) = 4

and g(2a + b) = (2a + b) - 4   ⇒   g(2a + 2) = 2a + 2 - 4   ⇒   g(2a + 2) = 2a - 2

                                                    ⇒  4 = 2a - 2

                                                          6 = 2a

                                                           3 = a

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .