TS EAMCET · Maths · Functions
If \(f: R \rightarrow C\) is defined by \(f(x)=e^{2 i x}\) for \(x \in R\), then \(f\) is (where \(C\) denotes the set of all complex numbers)
- A one-one
- B onto
- C one-one and onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(D) neither one-one nor onto
Step-by-step Solution
Detailed explanation
Given that, \(f(x)=e^{2 i x}\) and \(f: R \rightarrow C\). Function \(f(x)\) is not one-one, because after some values of \(x(i e, \pi)\) it will give the same values. Also, \(f(x)\) is not onto, because it has minimum and maximum values \(-1-i\) and \(1+i\) respectively. Hence,…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Three and four digit numbers are formed from the digits If is number of three digit even numbers with no digit repeated and is number of four digit even numbers with no digit repeated. Also represent the number of three digit odd numbers in which no digit is repeated and represent the number of four digit odd numbers in which no digit is repeated. ThenTS EAMCET 2021 Easy
- The number of ways of selecting a committee of persons from boys, girls and teachers such that the participation of number of boys, girls and teachers in that committee is equal, isTS EAMCET 2021 Easy
- If \(k=\frac{a+b}{a b}\) is a non-zero constant then the point which lies on the straight line \(\frac{x}{a}+\frac{y}{b}=1\) isTS EAMCET 2023 Easy
- \(\int_0^{\pi / 4}[\sqrt{\tan x}+\sqrt{\cot x}] d x\) is equal toTS EAMCET 2016 Medium
- If origin is the centre, \(X\)-axis is the major axis and \(\sqrt{\frac{2}{5}}\) is the eccentricity of an ellipse which passes through \((-3,1)\), then the equation of that ellipse isTS EAMCET 2018 Easy
- If \(\alpha\) is a root of multiplicity 3 of the equation \(x^5-8 x^4+25 x^3-38 x^2+28 x-8=0\), then \(\alpha^2-5 \alpha+6=\)TS EAMCET 2020 Medium
More PYQs from TS EAMCET
- One Debye is equal to how many coulomb meter?TS EAMCET 2021 Medium
- From the following compounds, the ones which contain both \(\mathrm{sp}\) and \(\mathrm{sp}^2\) hybridized carbons are
TS EAMCET 2022 Medium - Consider the following statements about the oxides of halogens A. At room femperature, \(\mathrm{OF}_2\) is thermally stable B. Order of stability of oxides of halogens is \(\mathrm{I}>\mathrm{Br}>\mathrm{Cl}\) C. \(\mathrm{I}_2 \mathrm{O}_5\) is used in the estimation of \(\mathrm{CO}\) D. \(\mathrm{ClO}_2\) is used as a bleaching agent The correct statement are.TS EAMCET 2023 Medium
- If \(\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathrm{d}\) are 4 vectors such that \(\mathbf{a} \cdot \mathbf{b}=0\), \(|\mathbf{a} \times \mathbf{c}|=|\mathbf{a}\|\mathbf{c}|,| \mathbf{a} \times \mathbf{d}|=| \mathbf{a}\| \mathbf{d}|\), then \([\mathbf{b c d}]=\)TS EAMCET 2018 Medium
- If the latus rectum through one of the foci of a hyperbola \(\frac{x^2}{9}-\frac{y^2}{b^2}=1\) subtends a right angle at the farther vertex of the hyperbola, then \(b^2=\)TS EAMCET 2025 Medium
- If \(3 x+6 y+2=0, x+y+1=0,2 x-y+3=0\) are three given lines then the point \(\left(\frac{-4}{3}, \frac{1}{3}\right)\) isTS EAMCET 2022 Medium