Question

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Diego plays center forward on his soccer team. On average, he scores 1.25 goals per match. The tally of his total goals for the season is given by function f(x) = 1.25(38 − x), where x is the number of matches he plays. What is the inverse of the function?
The inverse function is f-1(x) = . In the inverse function, the variable x represents the .

Answer 1

The inverse function f⁻¹(x) = 38 - x/1.25 and the variable x in the inverse function represents the number of goals for the season.

To answer the question, we need to find the inverse of the function.

How to find the inverse of the function?

Since on average, he scores 1.25 goals per match. The tally of his total goals for the season is given by function f(x) = 1.25(38 − x), where x is the number of matches he plays.

To find the inverse of the function, we represent f(x) by y.

So, f(x) = 1.25(38 − x)

y = 1.25(38 − x)

Dividing through by 1.25, we have

y/1.25 = 38 - x

Adding x to both sides, we have

x + y/1.25 = 38 - x + x

x + y/1.25 = 38

Subtracting y/1.25 from both sides, we have

x + y/1.25 - y/1.25 = 38 - y/1.25

x = 38 - y/1.25

Replacing y with x, we have

y = 38 - x/1.25

Replacing y with f⁻¹(x), we have

f⁻¹(x) = 38 - x/1.25

So, the inverse function f⁻¹(x) = 38 - x/1.25 and the variable x in the inverse function represents the number of goals for the season.

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