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

"see explanation"

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]}