How do you show that #f(x)=x-5# and #g(x)=x+5# are inverse functions algebraically and graphically?
1 Answer
Jan 2, 2018
Explanation:
#"using "color(blue)"composition of functions"#
#• " if "f(g(x)=x" and "g(f(x))=x#
#"then "f(x)" and "g(x)" are inverse functions"#
#f(g(x))=f(x+5)=x+5-5=x#
#g(f(x))=g(x-5)=x-5+5=x#
#rArrf(x)" and "g(x)" are inverse functions"#
#color(blue)"graphically"#
#"if "f(x)" and "g(x)" are reflections of each other in the line"#
#y=x" then they are inverse functions"#
#"any point "(a,b)" on " f(x)" should correspond to "(b,a)#
#"on "h(x)#
graph{(y-x+5)(y-x-5)(y-x)=0 [-10, 10, -5, 5]}
