By concepts of functions, the inverse of the rational function f(x) = (2 · x + 1)/(x - 4) is f⁻¹(x) = (4 · x + 1)/(x - 2), whose value at being evaluated at x = 3 is equal to 13.
How to determine the value of the inverse of a function
In this question we must determine the inverse of a given function and evaluate the resulting expression at a given value. First, we apply the following substitution:
f⁻¹(x) = x
x = f(x)
x = (2 · f⁻¹(x) + 1)/(f⁻¹(x) - 4)
Then we clear f⁻¹(x) within the expression:
x · (f⁻¹(x) - 4) = 2 · f⁻¹(x) + 1
x · f⁻¹(x) - 4 · x = 2 · f⁻¹(x) + 1
x · f⁻¹(x) - 2 · f⁻¹(x) = 4 · x + 1
f⁻¹(x) · (x - 2) = 4 · x + 1
f⁻¹(x) = (4 · x + 1)/(x - 2)
Lastly, we evaluate the function at x = 3:
f⁻¹(3) = (4 · 3 + 1)/(3 - 2)
f⁻¹(3) = 13
By concepts of functions, the inverse of the rational function f(x) = (2 · x + 1)/(x - 4) is f⁻¹(x) = (4 · x + 1)/(x - 2), whose value at being evaluated at x = 3 is equal to 13.
To learn more on inverse functions: https://brainly.com/question/2541698
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