Use f(x) and g(x) to find a formula for each expression. Identify each expression domain.

Question

Use f(x) and g(x) to find a formula for each expression. Identify each expression domain.

 

f(x) = √¯x-8,   g(x) = √¯x + 3

 

find a formula for (f + g)(x)

 

(f+g)(x)= ? 

Answer 1

f(x) = sqrt(x-8) and g(x) = sqrt(x+3).

Since we cannot take the square root of a negative number on the real x-y plane, we must have 

x - 8 >= 0 and x + 3 >= 0 implying the domain for f(x) is x in [8,inf) and for g(x) is x in [-3,inf). 

 

(f+g)(x) = f(x) + g(x) = sqrt(x-8) + sqrt(x+3) for x in [8,inf) = [8,inf)∩[-3,inf).