Question #29ecb

1 Answer
Oct 26, 2016

Answer:

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)#

Explanation:

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)#