Question

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

Answer 1

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