Which of the following functions is invertibl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) function $f: A 	o B$ is invertible if and only if it is a bijection,meaning it is both one-one (injective) and onto (surjective).$1$. For $f(x) =

Vedclass · Accepted Answer

$f(x) = 2^x$

Vedclass · Answer

(A) function $f: A 	o B$ is invertible if and only if it is a bijection,meaning it is both one-one (injective) and onto (surjective).$1$. For $f(x) = 2^x$,if we consider the domain as $\mathbb{R}$ and codomain as $(0, \infty)$,the function is strictly increasing (one-one) and covers all positive real values (onto). Thus,it is invertible.$2$. For $f(x) = x^3 - x$,the derivative $f'(x) = 3x^2 - 1$ changes sign at $x = \pm \frac{1}{\sqrt{3}}$,so it is not monotonic and not one-one on $\mathbb{R}$.$3$. For $f(x) = x^2$,$f(1) = f(-1) = 1$,so it is not one-one.Therefore,$f(x) = 2^x$ is the correct answer.

Which of the following functions is invertible?

Similar Questions

If $\alpha$ is the minimum value for which the inverse of $f(x)=x^2+3x-3$ exists in $[\alpha, \infty)$ and $g$ is the inverse of $f$, then find the value of $\frac{dg}{dx}$ at $x=\alpha+\frac{5}{2}$.

If the functions $f$ and $g$ are defined by $f(x) = 3x - 4$ and $g(x) = 2 + 3x$ for $x \in R$,then $g^{-1}(f^{-1}(5))$ is equal to

Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ is defined from $A$ to $B$ as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find $R^{-1}$.

Let $f$ and $g$ be two differentiable functions satisfying $g^{\prime}(5)=\frac{3}{4}$, $g(5)=6$ and $g=f^{-1}$. Then $f^{\prime}(6)$ is equal to

State with reason whether the following function has an inverse: $f: \{1,2,3,4\} \rightarrow \{10\}$ with $f = \{(1,10), (2,10), (3,10), (4,10)\}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module