TS EAMCET · Maths · Functions
Let \(Q\) be the set of all rational numbers in \([0,1]\) and \(f:[0,1] \rightarrow[0,1]\) be defined by \[ f(x)=\left\{\begin{array}{r} x \text { for } x \in Q \ 1-x \text { for } x \notin Q \end{array}\right. \] Then, the set \(S=\{x \in[0,21]:(f o f)(x)\}\) is equal to
- A \([0,1]\)
- B \(-Q\)
- C \([0,1]-Q\)
- D \((0,1)\)
Answer & Solution
Correct Answer
(A) \([0,1]\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\left\{\begin{array}{cc}x & \text { for } x \in Q \\ 1-x & \text { for } x \notin Q\end{array}\right.\) is defined for \[ f:[0,1] \rightarrow[0,1] \] If \(x\) is rational, then \[ \begin{array}{rlrl} f(x) & =x \\ \therefore \quad & f(f(x)) & =f(x)=x \end{array} \]…
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
- Length of the common chord of the circles \(x^2+y^2-6 x+5=\) and \(x^2+y^2+4 y-5=0\) isTS EAMCET 2024 Easy
- A plane \(\pi\) passing through the point \((1,1,1)\) is perpendicular to the line joining the points \((6,3,2)\) and \((1,-4,-9)\). If \(a x+b y+c z-23=0\) is the equation of the plane \(\pi\) then \(\mathrm{a}+\mathrm{b}-\mathrm{c}=\)TS EAMCET 2023 Easy
- If \(F_1\) and \(F_2\) are irreducible factors of \(x^4+x^2+1\) with real coefficients and \(\frac{x^3-2 x^2+3 x-4}{x^4+x^2+1}=\frac{A x+B}{F_1}+\frac{C x+D}{F_2}\), then \(A+B+C+D=\)TS EAMCET 2018 Medium
- If \(\int \frac{1}{x^4+8 x^2+9} d x\) \(=\frac{1}{k}\left[\frac{1}{\sqrt{14}} \tan ^{-1}(f(x))-\frac{1}{\sqrt{2}} \tan ^{-1}(g(x))\right]+c\), then \(\sqrt{\frac{k}{2}+f(\sqrt{3})+g(1)}=\)TS EAMCET 2024 Hard
- If \(x=2 \sqrt{2} \sqrt{\cos 2 \theta}\) and \(y=2 \sqrt{2} \sqrt{\sin 2 \theta}, 0 < \theta < \frac{\pi}{4}\) then the value of \(\frac{d y}{d x}\) at \(\theta=22 \frac{1}{2}^{\circ}\) isTS EAMCET 2025 Medium
- The focal distance of a point \((5,5)\) on the parabola \(x^2-2 x-4 y+5=0\) isTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- If the curves \(a x^2+b y^2=1\) and \(c x^2+d y^2=1\) intersect orthogonally, then \(\frac{b-a}{d-c}=\)TS EAMCET 2020 Medium
- Assertion (A) If the arguments of \(\bar{z}_1\) and \(z_2\) are \(\frac{\pi}{5}\) and \(\frac{\pi}{3}\) respectively, then \(\arg \left(z_1 z_2\right)\) is \(\frac{2 \pi}{15}\). Reason (R) For any complex number \(z\), \(\arg \bar{z}=\frac{\pi}{2}+\arg z\) The correct option among the following isTS EAMCET 2020 Easy
- A metallic wire with tension \(T\) and at temperature \(30^{\circ} \mathrm{C}\) vibrates with its fundamental frequency of \(1 \mathrm{kHz}\). The same wire with the same tension but at \(10^{\circ} \mathrm{C}\) temperature vibrates with a fundamental frequency of \(1.001 \mathrm{kHz}\). The coefficient of linear expansion of the wire isTS EAMCET 2002 Hard
-
The correct answer isTS EAMCET 2023 Easy - If the product of the slopes of the tangents drawn from an external point \(P\) to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is a constant \(k^2\), then the locus of \(P\) isTS EAMCET 2018 Medium
- Seven balls are drawn simultaneously from bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is :TS EAMCET 2006 Medium