Final answer:
The correct inverse function of the relativistic mass-speed relationship is option (c), which is f^(-1)(m) = √(m₀/m + 1), solving for the speed of a particle based on its relativistic mass.
Step-by-step explanation:
In the theory of relativity, the mass of a particle with speed v is given by m = f(v) = m₀ / ∙(1 - v²/c²), where m₀ is the rest mass of the particle, and c is the speed of light in a vacuum. To find the inverse function f^(-1)(m), which gives us the speed v as a function of the relativistic mass m, we must rearrange the formula to solve for v.
The correct inverse function is c) f^(-1)(m) = √(m₀/m + 1). This answer is obtained by isolating v on one side of the equation and then taking the square root to solve for the speed v. Note that option (a) does not account for the relativistic effects properly, option (b) does not represent an inverse function, and option (d) incorrectly adds to the velocity squared term instead of the correct relativistic subtraction.