[" If "f:R rarr R" be defined as "f(x)-=x+sin x+7" ,then check whether "f(x)" is one-one "],[" or many one "]

If f:R rarr R be defined as f(x)=sin(|x|) then which one of the following is correct?

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

f:R rarr R defined by f(x)=3x+2 this function is one-one?

If a function f: R to R is defined as f(x)=x^(3)+1 , then prove that f is one-one onto.

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

Let the function f:R rarr R be defined by f(x)=2x+sin x for x in R .Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one- to-one nor onto

Let a function f:R rarr R be defined by f(x) = 3 - 4x Prove that f is one-one and onto.