enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f: R \rightarrow R\) be a differentiable function that satisfies the relation \(f ( x + y )= f ( x )+ f ( y )-1, \forall x\), \(y \in R\). If \(f ^{\prime}(0)=2\), then \(|f(-2)|\) is equal to \(.........\).
- A \(6\)
- B \(9\)
- C \(3\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(f ( x + y )= f ( x )+ f ( y )-1\) \(f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\) \(f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(h)-f(0)}{h}=f^{\prime}(0)=2\) \(f^{\prime}(x)=2 \Rightarrow d y=2 d x\) \(y =2 x + C\) \(x =0, y =1, c =1\) \(y =2 x +1\)…
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
- Let the tangent to the circle \(C _{1}: x^{2}+y^{2}=2\) at the point \(M (-1,1)\) intersect the circle \(C _{2}\) : \(( x -3)^{2}+(y-2)^{2}=5\), at two distinct points \(A\) and \(B\). If the tangents to \(C _{2}\) at the points \(A\) and \(B\) intersect at \(N\), then the area of the triangle \(ANB\) is equal toJEE Mains 2022 Hard
- Let \(y=p(x)\) be the parabola passing through the points \((-1,0),(0,1)\) and \((1,0)\). If the area of the region \(\left\{(x, y):(x+1)^2+(y-1)^2 \leq 1, y \leq p(x)\right\}\) is \(A\), then \(12(\pi-4 A )\) is equal to \(.........\).JEE Mains 2023 Hard
- Let \(\mathrm{L}_1: \frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}\) and \(\mathrm{L}_2: \frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}\) be two lines.
Let \(L_3\) be a line passing through the point \((\alpha, \beta, \gamma)\) and be perpendicular to both \(L_1\) and \(L_2\). If \(L_3\) intersects \(\mathrm{L}_1\), then \(|5 \alpha-11 \beta-8 \gamma|\) equals :JEE Mains 2025 Hard - A group of students comprises of \(5\) boys and \(n\) girls. If the number of ways, in which a team of \(3\) students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is \(1750\), then \(n\) is equal toJEE Mains 2019 Hard
- Let \(S=\{z \in \mathbb{C}: z^2+4z+16=0\}\). Then \(\sum_{z \in S}|z+\sqrt{3}i|^2\) is equal to:JEE Mains 2026 Medium
- If the line \(ax + y = c,\) touches both the curves \(x^2 + y^2 = 1\) and \(y^2 - 4\sqrt 2 x ,\) then \(|c|\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- The positive value of the determinant of the matrix \(A\), whose \(A d j(A d j(A))=\left(\begin{array}{ccc}14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right)\), isJEE Mains 2022 Hard
- The number of real roots of the equation \(\mathrm{x}|\mathrm{x}-2|+3|\mathrm{x}-3|+1=0\) is :JEE Mains 2025 Medium
- If one real root of the quadratic equation \(81x^2 + kx + 256 = 0\) is cube of the other root, then a value of \(k\) isJEE Mains 2019 Hard
- The number of elements in the set \(\left\{x \in\left[0,180^{\circ}\right]: \tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right)\right\}\) is ___ .JEE Mains 2026 Easy
- If \(5 f(x)+4 f\left(\frac{1}{x}\right)=x^2-2, \forall x \neq 0\) and \(y=9 x^2 f(x)\), then \(y\) is strictly increasing in :JEE Mains 2024 Hard
- \(\mathop \smallint \limits_{\frac{\pi }{4}}^{\frac{{3\pi }}{4}} \frac{{dx}}{{1 + \cos x}} = \) . . . .JEE Mains 2017 Medium