State if the given functions f and g are inverses and give at least two sets of ordered pairs as the proofF(x)=5x and g(x)=x/5
Answer (1)
Yes, the functions f(x) = 5x and g(x) = x/5 are inverses of each otherExplanationTo verify that these functions are inverses, we need to check two conditions.1. Check f(g(x)) = xStart with g(x)[tex]\sf \: g(x) = \dfrac{x}{5}[/tex]Substitute g(x) into f[tex] \sf \: f(g(x)) = f(\dfrac{x}{5} ) = 5( \dfrac{x}{5}) = x[/tex]Therefore, f(g(x)) = x.2. Check g(f(x)) = xStart with f(x)[tex] \sf \: f(x) = 5x[/tex]Substitute f(x) into g[tex] \sf \:g (f(x)) = g(5x) = \dfrac{5x}{5} = x[/tex]Therefore, g(f(x)) = x.Since both conditions hold true, f and g are inverses of each other.Ordered Pairs1. For x = 1f(1) = 5 gives the ordered pair (1,5)g(5) = 1 gives the ordered pair (5,1)2. For x = 2f(2) = 10 gives the ordered pair (2,10)g(10) = 2 gives the ordered pair (10,2)These ordered pairs confirm the inverse relationship as (1,5) and (5,1), along with (2,10) and (10,2), show that they map back to each other correctly.
