Explain ( graphically) why x cosx is an onto function.

Which of the following is an onto function-

Number of onto and into functions

Define an onto function. Give one example. (A) A function f:A to B is said to be an onto function if AA b in EE a in A such that f(a)=b (or) if range of f = codomain of f then f is an onto function. Ex. f: R to R such that f(x) = 2x+3

All one-one function are onto functions

If f: A->B and g: B->C are onto functions, show that gof is an onto function.

If f: A->B and g: B->C are onto functions show that gof is an onto function.

If f:A rarr B and g:B rarr C are onto functions show that gof is an onto function.

Show that the function f(x) = x + cosx - a is an increasing function and hence deduce that the equation x+cosx = a has no positive root for a lt 1

Show that the function f(x) = x + cosx - a is an increasing function and hence deduce that the equation x+cosx = a has no positive root for a lt 1