Download App

Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsFunctions3 Marks
Question
If $f : R \rightarrow (0, 2)$ defined by $\text{f(x)}=\frac{\text{e}^{\text{x}}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}+1$ is invertible, find $f^{-1}.$
✓

Answer

$\text{A}=\{\text{x}\in\text{R}:-1\leq\text{x}\leq1\}$ and $f : A \rightarrow A, g : A \rightarrow A$ are two functions defined by $f(x) = x^2 $ and $\text{g(x)}=\sin\Big(\frac{\pi\text{x}}{2}\Big)$
Here, $f : A \rightarrow A$ is defined by
$f(x) = x^2$
Clearly f in not injective,
$\because\ \text{f}(1)=\text{f}(-1)=1$
So, $f$ is not bijective and hence not invertible.
Hence, $f^{-1}$ does not exist.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Functions→Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Write the converse, inverse and contrapositive of the following statement: "If it rains then the match will be cancelled."
→
With usual notations prove that $2\left\{a \sin ^2 \frac{C}{2}+c \sin ^2 \frac{A}{2}\right\}=a-b+c$.
→
In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.
→
Give examples of two one-one functions $f_1$ and $f_2$ from $R$ to $R$, such that $f_1 + f_2 : R \rightarrow R$. defined by $(f_1 + f_2)(x) = f_1(x) + f_2(x)$ is not one-one.
→
If A, B and C are independent events such that P(A) = P(B) = P(C) = p, then find the probability of occurrence of at least two of A, B and C.
→
Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.
→
Evalute the following integrals:
$\int\frac{\cos2\text{x}+\text{x}+1}{\text{x}^2+\sin2\text{x}+2\text{x}}\text{dx}$
→
Let f be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.
→
If $x=\phi(t)$ is a differentiable function of ' $t$ ', then prove that $\int f(x) d x=\int f[\phi(t)] \phi^{\prime}(t) d t$
→
Find the principal value of the following:
$\sec^{-1}\Big(2\tan\frac{3\pi}{4}\Big)$
→