SOLUTION: I must find the domain and range for: f(x) 3x-2 over 4+5x Domain: 4+5x=0 -4 both sides =5x=-4 divide 5 both sides x=-4 over 5 How do I find the range? Thank You

Algebra ->  Trigonometry-basics -> SOLUTION: I must find the domain and range for: f(x) 3x-2 over 4+5x Domain: 4+5x=0 -4 both sides =5x=-4 divide 5 both sides x=-4 over 5 How do I find the range? Thank You      Log On


   

Question 38890This question is from textbook
: I must find the domain and range for:
f(x) 3x-2 over 4+5x
Domain:
4+5x=0
-4 both sides
=5x=-4
divide 5 both sides
x=-4 over 5
How do I find the range?
Thank You This question is from textbook

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+%283x-2%29%2F%284%2B5x%29+

DOMAIN means what values of x can i put into this? Answer here is every single real value you could possibly think of except for one value... that value that makes the denominator zero. Because when the denominator is zero, the fraction goes to infinity... do any division by zero on your calculator and it will say ERROR.

So, 4+5x=0
5x = -4
x = -4/5

So, domain is "all real values of x except (-4/5). This is what you had, so well done.

As for the range: what values of "y" do we get out when we put every single x value in?

The best way to do this is to plot the graph: a visual aid will show you instantly any values not allowed etc. Algebraically, we need to find the inverse function, in other words, re-arrange f(x) so that we have x=f(y). So here goes:

+y+=+%283x-2%29%2F%284%2B5x%29+
+y%284%2B5x%29+=+%283x-2%29+
+4y%2B5xy+=+3x-2+
+4y%2B5xy-3x+=+-2+
+5xy-3x+=+-2-4y+
+x%285y-3%29+=+-2-4y+
+x+=+%28-2-4y%29%2F%285y-3%29+

so, again we have a denominator: 5y-3=0
5y=3
y=3/5

So range is "any real value of y except 3/5.

All clear?

jon.