Concept:The domain is the subset of R for which all operations in the function's formula make sense.The derivative of a function at a given point is the slope of the tangent line at that point.Formulae\(\displaystyle \frac{dy}{dx}=a^x\ log \ a\)Calculation:Statement I: Its domain is (-?, ?).The domain is the subset of R for which all operations in the function's formula make sense.Since 10 is a positive real constant, it can be raised to any real power, so the domain is not limited. It is R.So, Its domain is (-?, ?).Statement II: It is a continuous functionWe know that f(x) = 10x Derivative of f(x) is f'(x) = 10x log 10And now we have to find the points at which the derivative of f(x) is zero.? f'(x) = 10x log 10 = 0 As, we know that this can't happen.So, 10x is a continuous function for all real numbers.Statement II: It is differentiable at x = 0The derivative of a function at a given point is the slope of the tangent line at that point.Here, f(x) = 10x ? f'(x) = 10x log 10At x = 0, f'(0) = 100 log 10 ? log 10The derivative of function f(x) = 10x at x = 0 is log 10.So, It is differentiable at x = 0.? Statement I, II, and III are correct.