Question #29ecb

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Answer 1 · 2016-10-26T14:00:17

The product is $p(x)=(5x+7)*sqrt(2x-3)$ , its domain is $D_p=<3/2;+oo)$

The quotient is $q(x)=(5x-7)/sqrt(2x-3)$ , its domain is $D_q=(3/2;+oo)$

First we have to calculate the domains of $f(x)$ and $g(x)$ .

$f(x)$ is defined for all real numbers - $D_f=RR$

$g(x)$ is only defined when $2x-3>=0$

$2x>=3$

$x>=3/2$

$D_g=<3/2;+oo)$

The construction of product and quotient is just writing correct formulas using multiplication and division:

The product is $p(x)=(5x+7)*(sqrt(2x-3))$

The quotient is $q(x)=(5x-7)/sqrt(2x-3)$

The product is defined for those $x$ where both factors are defined, so its domain is $D_p=<3/2;+oo)$

The domain of $q(x)$ is smaller, because $g(x)$ cannot be zero (it is in the denominator), so you have to exclude $3/2$ from the domain.

Finally $D_q=(3/2;+oo)$