Question #6450c

1 Answer
Jim G.
Nov 27, 2017

#"see explanation"#

Explanation:

#(f.g)(x)=f(x)xxg(x)#

#color(white)((f.g)(x))=1/x xxx^2+5x=(x^2+5x)/x#

#"the denominator of "(f.g)(x)" cannot be zero as this"#
#"would make "(f.g)(x)" undefined"#

#(x^2+5x)/x=(cancel(x)(x+5))/cancel(x)#

#"the cancelling of the factor x denotes a hole at x = 0"#

#rArr"domain is "x inRR,x!=0#

#(f.g)(x)=x+5larrcolor(blue)"simplified"#

#"this is a linear function and is defined for all real"#
#"values"#

#rArr"range is "y inRR#
graph{(x^2+5x)/x [-20, 20, -10, 10]}

Related questions
Impact of this question
209 views around the world
You can reuse this answer
Creative Commons License