AP EAMCET · Maths · Functions
If \(f:[0,3] \rightarrow[0,3]\) is defined by \(f(x)\) \(=\left\{\begin{array}{ll}1+x, & 0 \leq x \leq 2 \\ 3-x, & 2 < x \leq 3\end{array}\right.\), then fof is
- A Continuous at \(x=1\)
- B Continuous at \(x=2\)
- C Discontinuous at \(x=1\) and \(x=2\)
- D Continuous on \([0,3]\)
Answer & Solution
Correct Answer
(C) Discontinuous at \(x=1\) and \(x=2\)
Step-by-step Solution
Detailed explanation
\[ \begin{gathered} g(x)=f(f(x))= \begin{cases}f(1+x) ; & 0 \leq x \leq 2 \\ f(3-x) & ; \quad 2 Using Eqs, (i), (ii), (iii), we get…
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 \(x^2 \tan ^{-1} \frac{y}{x}-y^2 \tan ^{-1} \frac{x}{y}=k\), then \(\left(\frac{d y}{d x}\right)_{(1,1)}=\)AP EAMCET 2023 Hard
- If the point \((2, \lambda)\) lies inside the circles \(x^2+y^2=13\) and \(x^2+y^2+x-2 y=14, \lambda\) lies in the setAP EAMCET 2022 Easy
- The Lines \(\mathrm{L}_1: \mathrm{y}-\mathrm{x}=0\) and \(\mathrm{L}_2: 2 \mathrm{x}+\mathrm{y}=0\) intersect the line \(\mathrm{L}_3: \mathrm{y}+2=0\) at P and \(Q\) respectively. The bisector of the angle between \(L_1\) and \(L_2\) divides the line segment PQ internally at R .
Statement-I \(\quad: \quad \mathrm{PR}: \mathrm{RQ}=2 \sqrt{2}: \sqrt{5}\)
Statement-II : In any triangle, bisector of an angle divides that triangle into two similar triangles.AP EAMCET 2025 Hard - If \(f(x)=\left\{\begin{array}{cc}4 x-5, & x \leq 2 \\ x-k, & x>2\end{array}\right.\) then the value of ' \(k\) ' if \(\lim _{x \rightarrow 2} f(x)\) may exist is equal toAP EAMCET 2020 Easy
- In \(\triangle \mathrm{ABC}\), if \(\mathrm{AB}: \mathrm{BC}: \mathrm{CA}=6: 4: 5\), then \(\mathrm{R}: r=\)AP EAMCET 2024 Easy
- If \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right]\) and \(\alpha A^2+\beta A=2 I\) for some \(\alpha, \beta, \in R\) then \(\alpha+\beta=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- If the equation of the pair of lines passing through \((1,1)\) and perpendicular to the pair of lines \(2 x^2+x y-y^2-x+2 y-1=0\) is \(a x^2+2 h x y+b y^2+2 g x+3 y=0\), then \(\frac{b}{a}=\)AP EAMCET 2025 Hard
- If \(\left|z+\frac{2}{z}\right|=2\), then the maximum value of \(|z|\) isAP EAMCET 2022 Medium
- A truck moving with a constant velocity \(12 \mathrm{~ms}^{-1}\) crosscs a car moving from rest with uniform acceleration \(2 \mathrm{~ms}^{-2}\). The distance the car has to travel from the starting point to cross the truck again isAP EAMCET 2023 Easy
- Which of the following is used in the estimation of carbon monoxide?AP EAMCET 2017 Medium
- \(a^n+b^n\) is divisible by if \(n\) is any odd positive integer.AP EAMCET 2020 Easy
- Which one of the following is not present in the nitration mixture?AP EAMCET 2019 Easy