f⁻¹(x)= x+25
f(x)= x-25
To find the inverse of a function, we need to switch the roles of x and y and then solve for y. So, for the given function f(x) = x + 25, we have:
y = x + 25 (switching x and y)
x = y + 25 (subtracting 25 from both sides)
y = x – 25 (subtracting y from both sides)
Thus, the inverse of the function f(x) = x + 25 is f⁻¹(x) = x – 25.
To see why this is the inverse, we can check by composing the two functions:
f(f⁻¹(x)) = f(x – 25) = (x – 25) + 25 = x
f⁻¹(f(x)) = f⁻¹(x + 25) = (x + 25) – 25 = x
Therefore, f⁻¹(x) = x – 25 is indeed the inverse of f(x) = x + 25.
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