Answer:
Option E. None of the above.
Explanation:
From the question given above, the following data were obtained:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
Recall:
When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e
f(x) × f¯¹(x) = 1
With the above information, we can determine the inverse of function given above as follow:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
f(x) × f¯¹(x) = 1
(x – 5)/(2x + 3) × f¯¹(x) = 1
f¯¹(x)(x – 5) / (2x + 3) = 1
Cross multiply
f¯¹(x)(x – 5) = (2x + 3)
Divide both side by (x – 5)
f¯¹(x) = (2x + 3) / (x – 5)
Thus, the inverse of the function is (2x + 3) / (x – 5).
Option E gives the correct answer to the question.