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)?

Solution:

Given functions are c(x) = 5/x - 2 and d(x) = x + 3

we know that d(x) is valid for all values of x

But c(x) is not valid for x = 2

For (cd)(x) = c(x)*d(x) = 5((x) × 3)/x - 2

Domain for (cd)(x) is all values of x except x = 2.

Also given f(x) = 7 + 4x and g(x) = 1/2x

(f/g)(x) = [7 + 4x] / [1/2x] = 2x(7 + 4x) / 1

(f/g)(5) = 2(5)(7 + 4(5)) /1

(f/g)(5) = 10(7 + 20) = 270

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)?

Summary:

If c(x) = 5/x-2 and d(x) = x + 3, the domain of (cd)(x) is all values of x except x = 2. And, if f(x) = 7 + 4x and g(x) = 1/2x, the value of (f/g)(5) is 270.