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

Question

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

 

f(x) = X^7/2 - X^5/2,     g(x) = X^3/2

 

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

 

(f + g)(x) = ?

Answer 1

f(x) = x^7/2 - x^5/2 = x^(6/2 + 1/2) - x^(4/2 + 1/2) = (|x|^3 - |x|^2) √(x)

 

The constraint on the domain of f(x) comes from the radical.

For f(x) to be real, x ≥ 0. Then the absolute value symbols can be discarded:

f(x) = (x^3 - x^2) √(x), x ≥ 0.

 

g(x) = x^3/2 = x^(2/2 + 1/2) = x √(x), x ≥ 0.

 

( f + g)(x) = f(x) + g(x)

 

= (x^3 - x^2 + x) √(x), x ≥ 0.

Answer 2

Hi Keith;

Each exponential has the number 2 in such denominators.  This means these are all square-roots.  Negative numbers cannot be square rooted.

The domain of f(x) and g(x) and (f+g)(x)≥0.

(f+g)(x)=x^7/2-x^5/2+x^3/2