Two functions are defined as shown below

Question

Question 1

Two functions are defined as shown below.

f = (Sqrt(x)+2) g = (g-2)²

a) Give the domain and range of f and . g

b) Write an expression for the function ( g+f )(x) and give its domain.

c) Find an expression for the function ( g o f)(x) and give its domain and range.

Answer 1

f(x) = sqr(x) +2

g(x) = (x-2)^2

a) domain of f is x>/=0, domain of g is any real number

b) (g+f)(x) = g(x) + f(x) = sqr(x) +2 + (x-2)^2 = sqr(x) +2 +x^2 +4x +4 = sqr(x) +x^2 +4x +6

domain = any non negative real number

c) g(f(x) = g(sqr(x) +2) -2)^2 = g(x) = (x-2)^2 = x^2 -4x +4

domain = any real number

range = any non negative real number