find natural domain and range for each function:

a) G(x)=(x^2-2*x+5)^(1/2)

b)h(x)=1/(1-sin(x))

c)H(x)=(sin(x^(1/2)))^(-2)

- Jan 8th 2010, 10:06 PMredcherryplz try this simple quest..the ans is different as i calculated.
find natural domain and range for each function:

a) G(x)=(x^2-2*x+5)^(1/2)

b)h(x)=1/(1-sin(x))

c)H(x)=(sin(x^(1/2)))^(-2) - Jan 8th 2010, 10:15 PMmr fantastic
- Jan 8th 2010, 10:29 PMredcherrytq for reply~
i just use this formula to find the roots which men the values of x..

(-b+(b^2-4*a*c))/2*a and got the ans x=1+4i and x=1-4i

but the ans for the domain is x=real number and the range y>=2. - Jan 8th 2010, 10:36 PMmr fantastic
What you posted is

**not**what I consider detailed working.

a) Domain: Solve $\displaystyle x^2-2x+5 \geq 0$.

b) Domain: All real numbers except those satisfying 1-sin(x) = 0.

c) Domain: All positive real numbers except those satisfying $\displaystyle \sin(\sqrt{x}) = 0$.

The details are left for you. I suggest you get ranges by drawing graphs. For a) note that $\displaystyle y=(x^2-2x+5)^{1/2} \Rightarrow y^2 = x^2 - 2x + 5$ and you should recognise a branch of a hyperbola. - Jan 8th 2010, 11:09 PMredcherryok..
for b) i got the domain x is not equal (2*n+1/2)*Pi but i didnt got the range

for c) the domain x is not equal (n*Pi)^2 and also didnt get the range.. - Jan 9th 2010, 02:37 AMmr fantastic
- Jan 9th 2010, 02:39 AMProve It