Suppose `f_1a n df_2` are non=zero one-one functions from `RtoRdot` is `(f_1)/(f_2)` necessarily one-one? Justify your answer. Here, `(f_1)/(f_2): RvecR` is given by `((f_1)/(f_2))(x)=(f_1(x))/(f_2(x))` for all `xRdot`

Suppose f_(1) and f_(2) are non-zero one-one functions from R to R. Is (f_(1))/(f_(2)) necessarily one- one? Justify your answer.Here,(f_(1))/(f_(2)):R rarr R is given by ((f_(1))/(f_(2)))(x)=(f_(1)(x))/(f_(2)(x)) for all x in R .

Let f be a function from R to R such that f(x)=cos(x+2) . Is f invertible? Justify your answer.

f:RrarrR given by f (x) = 2x is one-one function.

Show that if f_(1) and f_(2) are one-one maps from R to R, then the product f_(1)xx f_(2):R rarr R defined by (f_(1)xx f_(2))(x)=f_(1)(x)f_(2)(x) need not be one-one.

Show that if f_(1) and f_(1) are one-one maps from R to R, then the product f_(1)xf_(2):R rarr R defined by (f_(1)xf_(2))(x)=f_(1)(x)f_(2)(x) need not be one-one.

Given examples of two one-one functions f_(1) and f_(2) from R to R such that f_(1)+f_(2):R rarr R, defined by (f_(1)+f_(2))(x)=f_(1)(x)+f_(2)(x) is not one- one.

Let A=R-{3} and B=R-{1} .Consider the function f:A rarr B defined by f(x)=((x-2)/(x-3)) .Is f one-one and onto? Justify your answer.

Let f be a one-one function satisfying f'(x)=f(x) then (f^(-1))''(x) is equal to

If y=f(x) is one-one onto function, then: (f^-1@f)(x)=