FunctionHard
Question
Let f : R → R be a function defined by f(x) = x3 + x2 + 3x + sin x. Then f is:
Options
A.one - one and onto
B.one - one and into
C.many one and onto
D.many one and into
Solution
f(x) = x3 + x2 + 3x + sin x, x ∈ R
f′(x) = 3x2 + 2x + 3 + cos x
∵ 3x2 + 2x + 3 ≥
as a = 3 > 0 and D < 0
-1 ≤ cos x ≤ 1
so f′(x) > 0 ∀ x ∈ R
f(x) = + ∞
f(x) = - ∞
Hence f(x) is one-one and onto function (as f(x) is continuous function)
f′(x) = 3x2 + 2x + 3 + cos x
∵ 3x2 + 2x + 3 ≥
as a = 3 > 0 and D < 0-1 ≤ cos x ≤ 1
so f′(x) > 0 ∀ x ∈ R
f(x) = + ∞ f(x) = - ∞Hence f(x) is one-one and onto function (as f(x) is continuous function)
Create a free account to view solution
View Solution FreeMore Function Questions
If f(x) = = y, (a ≠ c), then f(y) equals to...Consider the function g(x) defined as g(x) (x(22011-1)-1) = (x + 1)(x2 + 1)(x4 + 1) . . .. (x22010 + 1) - 1, (|x| ≠...Let f(x) be a function whose domain is [- 5, 7]. Let g(x) = |2x + 5|, then domain of (fog) (x) is...If f : I → I,f (x) = x3 + 1, then f is -...Let $\alpha,\beta$ be the roots of the quadratic equation $12x^{2} - 20x + 3\lambda = 0,\lambda \in \mathbb{Z}$. If $\fr...