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Option E. None of the above.

Step-by-step 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.

c

step-by-step explanation: