Let f: R arrow R such that f(x)=x3+2 x2+7 x+5+3 sin x-4 cos x be a function then f(x) is

Question

Let f: R arrow R such that f(x)=x3+2 x2+7 x+5+3 sin x-4 cos x be a function then f(x) is (A) one-one and onto (B) one-one but not onto (C) onto but not one-one (D) neither one-one nor onto

Tardigrade Admin · Accepted Answer

f ( x )= x 3+2 x 2+7 x +5+3 sin x -4 cos x is an onto function ⇒ f prime( x )=3 x 2+4 x +7+3 cos x +4 sin x ≥ 3 x 2+4 x +2>0 ⇒ f ( x ) is an one-one function.

Q. Let $f : R \to R$ such that $f (x) = x^{3} + 2 x^{2} + 7 x + 5 + 3 sin x - 4 cos x$ be a function then $f (x)$ is

one-one and onto

one-one but not onto

onto but not one-one

neither one-one nor onto

$f (x) = x^{3} + 2 x^{2} + 7 x + 5 + 3 sin x - 4 cos x$ is an onto function
$\Rightarrow f^{'} (x) = 3 x^{2} + 4 x + 7 + 3 cos x + 4 sin x \geq 3 x^{2} + 4 x + 2 > 0$
$\Rightarrow f (x)$ is an one-one function.

Q. Let f:R→R such that f(x)=x3+2x2+7x+5+3sinx−4cosx be a function then f(x) is