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.
<h3>How to find the inverse of the function?</h3>
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.
Learn more about inverse function here:
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