Give examples of two one-one functions `f_(1)andf_(2)` from R to R such that `f_(1)+f_(2):RrarR` defined by :
`(f_(1)+f_(2))(x)=f_(1)(x)+f_(2)(x)`
is not one-one.

Give 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.

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.

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.

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.

If f:R rarr R defined by f(x)=(x-1)/(2) , find (f o f)(x)

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

If f:R rarr R is defined by f(x)=x/(x^2+1) find f(f(2))

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.

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 .

f:R^(+)rarr R^(+) defined by f(x)=1+2x^(2) this function is one-one?