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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