Let $f : R \to R$ be defined as $f (x) = 3^{- | x |} - 3^{x} + s g n (e^{- x}) + 2$ (Where sgn x denotes signum function of x). Then which one of the following is correct ?

f is injective but not surjective

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

f is surjective but not injective

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f is injective as well as surjective

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f is neither injective nor surjective

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Suggest Corrections

Similar questions

f : R \to R, f (x) = x^{2}

A = \{x : - 1 \leq x \leq 1\} a n d f : A \to A such that f (x) = x | x |

f : [- 1 / 2, 1 / 2, 1 / 2] \to [- π / 2, π / 2]

f (x) = \sin^{- 1} (3 x - 4 x^{3})

f : (0, \infty) \to (0, \infty)

f (x) = ∣ ∣ ∣ 1 - \frac{1}{x} ∣ ∣ ∣

f

f : N \to N

f (x) = 3 x^{2} + 2.

f (x)

Join BYJU'S Learning Program

Let f:R→R be defined as f(x)=3−|x|−3x+sgn(e−x)+2 (Where sgn x denotes signum function of x). Then which one of the following is correct ?