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

1 Answer
Nov 27, 2017

x=-1/5,1/5
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
-1/5 =x

EQUATION TWO (with -):
0=5x-1
1=5x
1/5=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 ().