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Option C. f¯¹(x) = (5x + 3)/2

Explanation:

f(x) = (2x – 3)/5

We can obtain the inverse of the above equation as follow:

Let f(x) be y.

Therefore,

F(x) = (2x – 3)/5

y = (2x – 3)/5

Next, we shall interchange the position of 'y' and 'x'. This is illustrated below:

y = (2x – 3)/5

x = (2y – 3)/5

Next, we shall make y the subject of the expression. This is illustrated below below:

x = (2y – 3)/5

Cross multiply

2y – 3 = 5x

Rearrange

2y = 5x + 3

Divide both side by 2

y = (5x + 3)/2

Therefore, the inverse of

f(x) = (2x – 3)/5 is f¯¹(x) = (5x + 3)/2

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