Question

If c(x)=5/x-2 and d(x)=x+3 what is the domain of (cd)(x)?. . And, if f(x)=7+4x and g(x)=1/2x, what is the value of (f/g)(5)?

Answer 1

Answer:

Domain of (cd)(x) is all real numbers values except 2.

The value of (f/g)(5) is 270

Step-by-step explanation:

Given c(x) and d(x) we have to find the domain of (cd)(x)

$c(x)=\frac{5}{x}-2$ and $d(x)=x+3$

The product of above two is

$(cd)(x)=c(x)d(x)=(\frac{5}{x-2})(x+3)$

The above function is defined at all real numbers values except 2 because that would make the denominator 0.  

Hence, domain of (cd)(x) is all real numbers except 2.

Given $f(x)=7+4x$ and $g(x)=\frac{1}{2x}$

we have to find the value of (f/g)(5)

$\text{(f/g)x=}\frac{7+4x}{\frac{1}{2x}}=2x(7+4x)$

put x=5

$\text{(f/g)(5)=}2x(7+4x)=2(5)(7+4(5))=10(27)=270$

Answer 2

1. The value of (cd)(x) is equal to the product of c(x) and d(x) which is equal to,
                                         5(x + 3) / (x - 2)
The function can take all real numbers except 2 because that would make the denominator 0. 

2. To answer, substitute first 5 to the given functions,
                      f(x) = 7 + 4x = 7 + 4(5) = 27
                      g(x) = 1/2x = 1 / (2)(5) = 1/10
Dividing 27 by 1/10 is 270.