Let a function f:1,∞→0,∞ be defined by fx=1-1/x. Then f is

Correct answer: (B) both injective as well as surjective. fx=1-1/x=(x-1)/x=(x-1)/x f^(′) x =1/(x^2) f^(′) x >0 ∴fx is injective and range of function is 0,∞Hence, injective and surjective

Q6 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

Let a function $f : (1, \infty) \to (0, \infty)$ be defined by $f (x) = |1 - \frac{1}{x}|$ . Then $f$ is

A
injective but not surjective
Correct answer
B
both injective as well as surjective
C
not injective but it is surjective
D
neither injective nor surjective

Solution

f (x) = |1 - \frac{1}{x}| = |\frac{x - 1}{x}| = \frac{x - 1}{x}

f^{'} (x) = \frac{1}{x^{2}}

f^{'} (x) > 0

∴ f (x)

is injective and range of function is

(0, \infty)

Hence, injective and surjective

Hence, the correct answer is option: 'B'.

Let a function f:1,∞→0,∞ be defined by fx=1-1x. Then f is

Solution

More Functions Questions

Let a function $f : (1, \infty) \to (0, \infty)$ be defined by $f (x) = |1 - \frac{1}{x}|$ . Then $f$ is