Step-by-step explanation:f^-1 means the inverse function that finds the x responsible for the creation of a given y (functional result) value.y = 3x - 13x = y + 1x = 1/3(y + 1)and now we rename x to y and y to x, so that we get a normal function definition :y = 1/3(x + 1) = (1/3)x + 1/3now we create the first derivative d/dx of this function :y' = 1/3since both f(x) and f^‐1(x) are line functions with a constant slope, it is not surprising that the first derivative (the function of the slope of the base function) is a constant function. so, for any value of x (incl. the requested x = 11) d/dx f^-1(x) = 1/3.therefore also d/dx f^-1(11) = 1/3.y = 2×sqrt(x)sqrt(x) = y/2x = y²/4again we rename the variables, so that we get a normal function definition for the inverse function :y = x²/4the first derivative is :y' = 2x/4 = x/2so, d/dx f^-1(6) = 6/2 = 3