SOLUTION: For f(x)=√(x-3) and g(x)=x^3 a) the domain of f b) the domain of g c) (f-g)(x) d) (fg)(x) e) the domain of (f/g)(x)

Algebra ->  Functions -> SOLUTION: For f(x)=√(x-3) and g(x)=x^3 a) the domain of f b) the domain of g c) (f-g)(x) d) (fg)(x) e) the domain of (f/g)(x)      Log On


   

Question 102768: For f(x)=√(x-3) and g(x)=x^3
a) the domain of f
b) the domain of g
c) (f-g)(x)
d) (fg)(x)
e) the domain of (f/g)(x)
Found 2 solutions by edjones, Nate:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
f[x]=sqrt[x-3], g[x]=x^3
a. domain f: X[3,infinity)
.
b. domain g: X(-infinity,infinity)
.
c. sqrt(x-3)-x^3
.
d. x^3*sqrt(x-3)
.
e. domain [f/g]: X[3,infinity)
.
Ed

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
For f(x)=√(x-3) and g(x)=x^3
a) the domain of f
The only limitation to this equation is the radical.
x - 3 >= 0
x >= 3
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Csqrt%28x+-+3%29%29
b) the domain of g
There are no limitations in the cubic equation.
All Real Values
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3%29
c) (f-g)(x)
Once again, the only limitation to this equation is tbe radical.
x >= 3
graph%28300%2C300%2C-5%2C5%2C-40%2C5%2Csqrt%28x+-+3%29+-+x%5E3%29
d) (fg)(x)
Again, only limitation is the readical.
x >= 3
graph%28300%2C300%2C-5%2C5%2C-6%2C60%2Csqrt%28x+-+3%29x%5E3%29
e) the domain of (f/g)(x)
The two limitations are the radical and the denominator.
x >= 3 and x can not be zero ....
x >= 3
graph%28300%2C300%2C-5%2C5%2C0%2C.125%2Csqrt%28x+-+3%29%2Fx%5E3%29