Find all differentiable functions f : R ---> R such that (f composed f) = f.

R = All Real Numbers

(f composed f) = the function f composed with itself

Solution Preview

because,
f composed f = fof = f(f(x)
according to the question,
f(f(x)) = f(x)
What does this mean? => It implies that whatever is the value of function f at x, the same value ...

Solution Summary

The diffrentiabilty of a given function is examined.

...Find the altitude of the satellite and the rate at which the altitude is changing at this instant. 1. Functions f, g, and h are continuous and differentiable...

... given first order differential equation this is solved using Laplace transform methods going through to find the Laplace domain transfer function, finding the ...

... we get is the solution for the differential equation. ... a swimming pool is defined by the function, f(x ... use the arc length formula.) First we find the derivative ...

... Theorem are satisfied for each of the functions on the given intervals, and find the value of ... continuous over their domains, F(x) is differentiable over (-2 ...

... of the function: f(x) = arccot(tan(2x + 3)). Dear student, please refer to the attachment for the solutions. Problem: Find the solution of the differential...

... (2) Find the solutions of the differential equations ... x (0) = 0 1) We know that the Laplace transform of a convolution product of two functions is the ...

... "Assume that the equation determines a differentiable function f such that y=f(x), find y'.". The following functions are called implicit functions. ...

... 5. Solve the differential equation, y is a function of x y ... 1. Find both the first and second order differentials (y' and y") for the following functions: ...

... Let the given function be Ly = (e^t + t)^2 where L is the operator d^/dx ... One can find a particular solution to each of the individual differential equation ...

... is necessary to have BOTH sin and cos functions in the ... 1). Given the differential equation for y = y ( x) 1 ... e − bx / x 2 , x > 0 ; a) Find the complementary ...