Question

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

Answer 1

The true statement is (g•f)(x) = x ⇒ answer D

Step-by-step explanation:

Let us revise the relation between a function and its inverse

• 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

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