Given f(x)=|x| and g(x)=5x+1 Find f(g(x)) and domain and range?

1 Answer
Nov 27, 2017

x=15,15
DOMAIN: (,+)
RANGE: (1,+)

Explanation:

f(g(x)) is substituting 5x+1 into the x variable in f(x)=|x|

You would start off by doing this:
f(x)=|5x+1|

To solve this, you would change the + sign into a sign and solve both equations

EQUATION ONE (with +):
0=5x+1
1=5x
15=x

EQUATION TWO (with ):
0=5x1
1=5x
15=x

The domain is the set of all possible x-values and the range is the set of all possible y-values.

So the domain of f(g(x)) (also known as f(x)=|5x+1|) would be
(,+) or All Real Numbers because the graph starts from negative infinity and proceeds on to positive infinity.

The range would be (1,+) because the graph starts at 1 on the y axis and goes up to infinity ().