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 (#∞#).