Answer :
Given a linear function f(x) = mx + b, the slope of its inverse function f⁻¹(x) depends on the reciprocal of the slope of f.
In general, the inverse of a linear function f(x) = mx + b can be represented as f⁻¹(x) = (x - b)/m, where m is the slope of the original function f.
Exercise 57 asks for the derivative ¹(x) of f(x), which is simply m, as the derivative of a linear function is equal to its slope.
Exercise 58 states that if the slope of f is 3, the slope of f⁻¹ will be the reciprocal of 3, which is 1/3.
Exercise 59 suggests that if the slope of f is m, the slope of f⁻¹ will be 1/m, as the slopes of a function and its inverse are reciprocals.
Exercise 60 confirms that if the slope of f is m, the slope of f⁻¹ will be 1/m.
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