SOLUTION: Hi! Use the given functions to answer the following questions. (Enter NONE in any unused answer blanks.)Evaluate f(x)f(x) and g(x)g(x) and give their domains: f(x) = x/(x + 3

Algebra ->  Functions -> SOLUTION: Hi! Use the given functions to answer the following questions. (Enter NONE in any unused answer blanks.)Evaluate f(x)f(x) and g(x)g(x) and give their domains: f(x) = x/(x + 3      Log On


   

Question 198279: Hi!
Use the given functions to answer the following questions. (Enter NONE in any unused answer blanks.)Evaluate f(x)f(x) and g(x)g(x) and give their domains:
f(x) = x/(x + 3), g(x) = 2 x - 3
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

f%28x%29+=+x%2F%28x+%2B+3%29 Start with the given function.


f%28x%29f%28x%29+=+f%28x%29%28x%2F%28x+%2B+3%29%29 Multiply both sides by f(x).


f%28x%29f%28x%29+=+%28x%2F%28x+%2B+3%29%29%28x%2F%28x+%2B+3%29%29 Plug in f%28x%29+=+x%2F%28x+%2B+3%29


f%28x%29f%28x%29+=+%28x%5E2%29%2F%28%28x+%2B+3%29%28x+%2B+3%29%29 Multiply


Take note that x%3C%3E-3 since this causes a division by zero. So the domain is x can be any real number BUT x cannot equal -3.






# 2

g%28x%29=2x-3 Start with the given function.


g%28x%29g%28x%29=g%28x%29%282x-3%29 Multiply both sides by g(x).


g%28x%29g%28x%29=%282x-3%29%282x-3%29 Plug in g%28x%29=2x-3


g%28x%29g%28x%29=%282x%29%282x%29%2B%282x%29%28-3%29%2B%28-3%29%282x%29%2B%28-3%29%28-3%29 FOIL


g%28x%29g%28x%29=4x%5E2-6x-6x%2B9 Multiply


g%28x%29g%28x%29=4x%5E2-12x%2B9 Combine like terms.


Take note that there are no division by variables or square roots, logs, etc.. that would cause a division by zero or any other undefined property. So we don't need to worry about any restrictions.

So the domain is all real numbers.