Unknown g (x) = ax + b and g (g (x)) = 16x - 15. Calculate the value of a and b.

G (g (x)) = 16x-15

means that when you subsituted g (x) for x in g (x), you got 16x-15

a (ax+b) + b=16x-15

distribute

xa^2+ab+b=16x-15d

we look at the x terms

therefor

xa^2=16x

a^2=16

a=-4 or 4

we will find out

look a constant terms

ab+b=-15

undistribute b

b (a+1) = - 15

if a is - 4 then

b (-4+1) = - 15

b (-3) = - 15

b=5

if a=4 then

b (4+1) = - 15

b (5) = - 15

b=-3

so

g (x) = - 4x+5 or

g (x) = 4x-3

if a=-4, b=5

if a=4, b=-3