For the functions f(x)= sqrt x-1 and g(x)=5x

Question

For the functions f(x)= sqrt x-1 and g(x)=5x Find the following. 

 

a) (f*g)(x) and its domain.

 

b) (g*f)(x) and its domain. 

Answer 1

f(x) = √(x-1), g(x) = 5x

 

(f*g) = √(5x-1)

 

domain  5x- 1 ≥ 0

=> x  ≥ 1/5

=> x; [1/5, ∞)

 

(g*f) = 5√(x-1)

 

domain x-1 ≥ 0

 

x ≥ 1

x; [1,∞)

 

:)

Answer 2

Hi Georgina;

f(x)= √(x-1) and g(x)=5x

The domain of f(x) is limited by the first equation.  The square root of any number less than zero does not exist.

x-1=0

x=1

Domain is x>1

(1, +infinity)

(f*g)x=

(g*f)x=

The * means to me that we are multiplying the equations together.

(f*g)x=[√(x-1)](5x)

(g*f)x=(5x)[√(x-1)]

As you can see, both equations are the identical.  The only difference is organization.