Question

Are F(x) and G(x) inverse functions across the domain (5,+[infinity])(5,+[infinity])?

F(x)=√x−5​+4
G(x)=(x−4)²+5

a) Yes, because (x−4)²+5
b) No, because G(x)−5+4⋅x
c) No, because √x−5​+4 -(x−4)²+5
d) Yes, because G(x)−5+4=x

Answer 1

Yes, F(x) and G(x) are inverse functions across the domain (5, +[infinity]).

Step-by-step explanation:

Yes, F(x) and G(x) are inverse functions across the domain (5, +[infinity]). To determine if two functions are inverse functions, we need to show that when one function is applied to the other, we get the original input value back.

Let's check if F(G(x)) = x for x > 5:

F(G(x)) = F((x-4)²+5) = √((x-4)²+5-5)+4 = √(x-4)²+4

Since the square root function (√) undoes the square (^2) operation, we can simplify further:

= (x-4)+4 = x - 4 + 4 = x

Therefore, F(x) and G(x) are inverse functions for x > 5.