WBJEE · Maths · Functions
The function \(f(x)=x^{2}+b x+c,\) where \(b\) and \(c\) real constants, describes
- A one-to-one mapping
- B onto mapping
- C not one-to-one but onto mapping
- D neither one-to-one nor onto mapping
Answer & Solution
Correct Answer
(D) neither one-to-one nor onto mapping
Step-by-step Solution
Detailed explanation
Given function is \[ f(x)=x^{2}+b x+c \] It is a quadratic equation in \(x\). So, we will get a parabola either downward or upward. Hence, it is a many one mapping and not onto mapping. Hence, it is neither one-to-one nor onto mapping.
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
- If \(\left|\begin{array}{ccc}-1 & 7 & 0 \\ 2 & 1 & -3 \\ 3 & 4 & 1\end{array}\right|=A\). Then \(\left|\begin{array}{ccc}13 & -11 & 5 \\ -7 & -1 & 25 \\ -21 & -3 & -15\end{array}\right|\) is \begin{array}{l} \hline \end{array} \(\left(I_{3}\right.\) denotes the det of the identity matrix of order 3 )WBJEE 2018 Medium
- If the sum of two unit vectors is a unit vector, then the magnitude of their difference isWBJEE 2017 Easy
- Two circle \(S_1=p x^2+p y^2+2 g^{\prime} x+2 f^{\prime} y+d=0\) and \(S_2=x^2+y^2+2 g x+2 f y+d^{\prime}=0\) have a common chord \(P Q\). The equation of \(\mathrm{PQ}\) isWBJEE 2022 Easy
- A double ordinate \(\mathrm{PQ}\) of the hyperbola \(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1\) is such that \(\Delta \mathrm{OPQ}\) is equilateral, \(\mathrm{O}\) being the centre of the hyperbola. Then the eccentricity e satisfies the relationWBJEE 2020 Easy
- If \(a, b, c\) are in G. P. and \(\log a .-\log 2 b, \log 2 b-\log 3 c, \log 3 c-\log a\) are in A. P., then \(a, b, c\) are the lengths of the sides of a triangle which isWBJEE 2022 Hard
- If the point \((2 \cos \theta, 2 \sin \theta)\) for \(0 \in(0,2 \pi)\) lies in the region between the lines \(x+y=2\) and \(x-y=2\) containing the origin, then \(\theta\) lies inWBJEE 2015 Hard
More PYQs from WBJEE
- The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places isWBJEE 2010 Medium
- The velocity-time graph for a body of mass 10 kg is shown in the figure. Work done on the body in the first two seconds of motion is
WBJEE 2025 Medium - Two cells \(A\) and \(B\) of emf \(2 \mathrm{V}\) and \(1.5 \mathrm{V}\) respectively, are connected as shown in figure through an external resistance \(10 \Omega\) The internal resistance of each cell is \(5 \Omega\). The potential difference \(E_{A}\) and \(E_{B}\) across the terminals of the cells \(A\) and \(B\) respectively are
WBJEE 2015 Medium - 2-methylpropane on monochlorination under photochemical condition giveWBJEE 2013 Easy
- Standard deviation of \(n\) observations \(a_{1}, a_{2}, a_{3}, \ldots, a_{n}\) is \({\sigma} .\) Then, the standard deviation of the observations \(\lambda a_{1}, \lambda a_{2}, \ldots, \lambda a_{n}\) isWBJEE 2016 Medium
- The electronic configuration of \(\mathrm{Cu}\) isWBJEE 2014 Easy