Functions of f and g

Question

if f(x)= 4x-1 and g(x)= x+1/4

(a) What are f(g(x)) and g(f(x))?

(b) Are f(x) and g(x) inverse functions?

Answer 1

f(x) = 4x - 1   and    g(x) = x + ¼

 

f(g(x)) = f(x + ¼) = 4(x + ¼) - 1 = 4x + 1 - 1 = 4x

 

g(f(x)) = g(4x - 1) = (4x - 1) + ¼ = 4x - 3/4

 

If f(x) and g(x) are inverse functions, then 

f(g(x)) = g(f(x)) = x.  So, the given functions are not inverses of each other.