Let fx be a linear function fx ax b for constants a and b

Let f(x) be a linear function, f(x) = ax + b for constants a and b. Show that f(f(x)) is a linear function. Compute the composition f(f(x)). f(f(x)) = a^2x + ab + b The function f(f(x)) is a linear function because: The variable x has a degree of 2. The coefficient of x is constant. The variable x has a degree of 1. The variable x has a coefficient. The function has a constant term. (b) Find a function g(x) such that g(g(x)) = 2x - 7. g(x) =

Solution

a) f(x) = ax +b

f(f(x)) = a(ax+b) +b

= a^2x +ab +b

= a^2*x + (ab +b)

It is a linear function as it degree of variable x is 1.

b) g(x) = 2x -7

g(g(x)) = 2(2x -7) -7

= 4x - 14 -7

= 4x - 21