If f(x) and g(x) are inverse functions of each other, which of the following statements is true?

A.) f(x) divided by g(x) =1

B.) f(x) = -g(x)

C.) (f•g)(x) = 1 (The back dot does not mean times, it means f of g of x)

D.) (g•f)(x) = x

The inverse of the function f(x) = y is g(y) = x
The function and its inverse are reflections across the line y = x
The graph of f(x) and the graph of its inverse g(x) are intersected at a point lie on the line y = x
f(g(x)) = g(f(x)) = x

Example:

g(x) is the inverse function of f(x)

∵ f(x) = x - 5

∵ f(x) = y

∴ y = x - 5

To find the inverse switch x and y and find y

∵ x = y - 5

- Add 5 to both sides

∴ x + 5 = y

∴ g(x) = x + 5

Let us find f(g(x)) and g(f(x)0

To find f(g(x)) substitute x in f(x) by g(x)

∵ f(g(x)) = (x + 5) - 5

∴ f(g(x)) = x + 5 - 5

∴ f(g(x)) = x

To find g(f(x)) substitute x in g(x) by f(x)

∵ g(f(x)) = (x - 5) + 5

∴ g(f(x)) = x - 5 + 5

∴ g(f(x)) = x

Now let us solve the question

∵ f(x) and g(x) are inverse functions of each other

∴ f(g(x)) = g(f(x)) = x

The true statement is (g•f)(x) = x

Learn more:

You can learn more about the inverse function in brainly.com/question/2456302

#LearnwithBrainly

If f(x) and g(x) are inverse functions of each other, which of the following statements is true?A.) f(x) divided by g(x) =1B.) f(x) = -g(x)C.) (f•g)(x) = 1 (The back dot does not mean times, it means f of g of x)D.) (g•f)(x) = x