Question

Let f(x)= 1/4x + 2 and g (x) = 4x - 2. Which of the following statements is true?

A- f (x) and g(x) are not inverses of each other since g (f(x))= x + 3/2
B- f (x) and g (x) are inverses of each other since f (g (x))- g (f (x))- x
C- f (x) and g (x) are not inverses of each other since g (f(x))= x + 6
D- f(x) and g(x) are inverses of each other since f (g (x))= g(f (x))= x + 3/2

Answer 1

Option B is the correct statement. f(x) and g(x) are inverses of each other since their compositions result in x.

Step-by-step explanation:

Option B

is the correct statement. In order for two functions to be inverses of each other, their compositions should result in the identity function. To verify this, we can find the composition of f(g(x)) and g(f(x)) and check if it equals x. For f(g(x)), substitute g(x) into the function f(x), which gives us 1/4(4x-2) + 2. Simplifying this expression gives us x, which means f(g(x)) = x. Similarly, for g(f(x)), substitute f(x) into the function g(x), which gives us 4(1/4x+2) -2. Simplifying this expression also gives us x, which means g(f(x)) = x. Since both compositions result in x, we can conclude that f(x) and g(x) are inverses of each other.