Which pair of functions are inverses of each other?A.𝑓(𝑥)=2𝑥−6f(x)= x2​ −6 and 𝑔(𝑥)=𝑥+62g(x)= 2x+6​ B.f(x) = 2x – 9 and 𝑔(𝑥)=𝑥+92g(x)= 2x+9​ C.𝑓(𝑥)=𝑥3+4f(x)= 3x​ +4 and g(x) = 3x – 4D.𝑓(𝑥)=𝑥35f(x)= 53 x​ ​ and g(x) = 5x3SUBMITarrow_backPREVIOUS

To determine which pair of functions are inverses of each other, we need to check if the composition of the two functions results in the identity function. The identity function is a function that always returns the same value that was used as its argument. In other words, if f and g are a pair of functions and are inverses of each other, then the following two equations should be true:

1. f(g(x)) = x for all x in the domain of g
2. g(f(x)) = x for all x in the domain of f

Let's check each pair:

A. 𝑓(𝑥)=2𝑥−6 and 𝑔(𝑥)=𝑥/2+3 f(g(x)) = 2*(x/2+3) - 6 = x + 6 - 6 = x g(f(x)) = (2x - 6)/2 + 3 = x - 3 + 3 = x So, f and g are inverses of each other.

B. f(x) = 2x – 9 and 𝑔(𝑥)=𝑥/2+9/2 f(g(x)) = 2*(x/2+9/2) - 9 = x + 9 - 9 = x g(f(x)) = (2x - 9)/2 + 9/2 = x - 9/2 + 9/2 = x So, f and g are inverses of each other.

C. 𝑓(𝑥)=𝑥/3+4 and g(x) = 3x – 4 f(g(x)) = (3x - 4)/3 + 4 = x - 4/3 + 4 = x + 4/3 g(f(x)) = 3*(x/3 + 4) - 4 = x + 12 - 4 = x + 8 So, f and g are not inverses of each other.

D. 𝑓(𝑥)=𝑥/5^3 and g(x) = 5x^3 f(g(x)) = (5x^3)/5^3 = x^3/5^2 = x/25 g(f(x)) = 5*(x/5^3)^3 = 5x^3/5^3 = x^3/5^2 = x/25 So, f and g are not inverses of each other.

Therefore, the pairs A and B are inverses of each other.