Question

Can you help with precalc questions?!

Answer 1

The domain of a function is the set of values for which it is defined. When the function involves a square root, the square root is not defined for negative arguments, so the domain cannot include any values that make the square root be of a negative number.

Similarly, a rational function will be undefined where its denominator is zero.

1) h(x) is defined for 2x+10 > 0, or x > -5. The marked choice is appropriate.

2) The product of the two functions will be

`(f\cdot g)(x)=(√(x+3))/(x)\cdot(√(x+3))/(2x)=(√(x+3)√(x+3))/((x)(2x))\\\\=(x+3)/(2x^2)\qquad\text{3rd choice}`

3) The domain of f(x) is x≠0. The domain of g(x) is 3x-9>0, or x > 3. The latter includes the former, so the domain is ...

... (3, ∞)