Unknown g (x) = ax + b and g (g (x)) = 16x - 15. Calculate the value of a and b.
Mathematics · High School · Tue Nov 03 2020
Answered on
For solving this question we take given information by the question
Given g(x) =ax+b ……..(1)
g(g(x))=16x-15 ……(2)
For finding the value of “a”and “b” we use equation (1) and solve g(g(x)) substitute value of “g(x)”in “g(g(x))”by the equation (1)
g(g(x))=a(ax+b)+b …….(3)
By the equation (2)and(3) both are equavelent to g(g(x)) so we do equation (2)=(3)
16x-15 =a^2x+ab +b
By the comparison of x multiples and constants we get
a^2=16
a=√16 or (a)^2=(4)^2
a=4 ans
And ab+b=-15
b(a+1)=-15
By the putting value of" a "
b(4+1)=-15
b(5)=-15
b=-(15/5)
b=-3 ans