Show that `f(x)=3x+5` for all `xinQ`, is one-one.

Consider the following statements : Statement 1 : The function f:IRtoIR such that f(x)=x^(3)" for all "x""inIR is one-one. Statement 2 : f(a)impliesf(b)" for all "a,binIR if the function f is one-one. Which one of the following is correct in respect of the above statements ?

Show that the function f:R rarr R given by f(x)=cos x for all x in R, is neither one- one nor onto

Show f:R rarr R " defined by " f(x)=x^(2)+x " for all " x in R is many-one.

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

Show that the function f:Z rarr Z defined by f(x)=x^(2)+x for all x in Z, is a many-one function.

Show that the function f:R rarr R defined by f(x)=3x^(3)+5 for all x in R is a bijection.

Show that the function f:R rarr R defined by f(x)=3x^(3)+5 for all x in R is a bijection.

Show that f(x) = 3x + 5 is a strictly increasing function on R

If f(x)=|x|^(3), show that f(x) exists for all real x and find it.