SOLUTION: a. Find the domain of the function defined by {{{ F(x) = x/sqrt(x+20) + sqrt(5-x) }}} Write your answer in interval form. b. Find the average rate of change, A, of {{{ g(x) = 2x

Algebra ->  Functions -> SOLUTION: a. Find the domain of the function defined by {{{ F(x) = x/sqrt(x+20) + sqrt(5-x) }}} Write your answer in interval form. b. Find the average rate of change, A, of {{{ g(x) = 2x      Log On


   

Question 948403: a. Find the domain of the function defined by +F%28x%29+=+x%2Fsqrt%28x%2B20%29+%2B+sqrt%285-x%29+ Write your answer in interval form.
b. Find the average rate of change, A, of +g%28x%29+=+2x%5E2+-5x+ from +x=a+ to +x=a%2Bh+ Don't forget to simplify your answer. (h should not be in the denominator answer)
Thank you
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
a:

The expressions inside the square roots must be non-negative.
x%3E=-20 and x%3C=-5.
The x values in both of those are highlight%28-20%3C=x%3C=-5%29. That is the domain.


b:

The average rate of change on the described interval of g.
%282%28a%2Bh%29%5E2-5%28a%2Bh%29-%282%28a%29%5E2-5%28a%29%29%29%2F%28%28a%2Bh%29-a%29

%282%28a%5E2%2B2ah%2Bh%5E2%29-5a-5h-%282a%5E2-5a%29%29%2Fh

%282a%5E2%2B4ah%2B2h%5E2-5a-5h-2a%5E2%2B5a%29%2Fh
Look for the additive inverses in numerator.

%284ah%2B2h%5E2-5h%29%2Fh

%28h%2Fh%29%284a%2B2h-5%29

highlight%284a%2B2h-5%29

Keep track of the variables and expressions in each step.