TS EAMCET · Maths · Functions
Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}x^2-4 x+3, & \text { if } x < 2 \ x-3, & \text { if } x \geq 2\end{array}\right.\) Then the number of real numbers \(x\) for which \(f(x)=8\) is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(f(x)=8\) ...(i) For \(x < 2\) \(\begin{aligned} & f(x)=x^2-4 x+3=8 \\ & x^2-4 x-5=0 \\ & (x-5)(x+1)=0 \\ & x=-1 ; 5\end{aligned}\) \(\because x < 2\) \(\therefore x=5\) not possible and for \(x \geq 2\) \(f(x)=x-3=8 \Rightarrow x=11\) \(\therefore\) Number of solutions \(=2\)
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
- \(\lim _{x \rightarrow 3 / 2} \frac{\left(4 x^2-6 x\right)\left(4 x^2+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=\)TS EAMCET 2024 Medium
- If \(\alpha, \beta\) are non-real cube roots of 2 , then \(\alpha^6+\beta^6\) equalsTS EAMCET 2015 Medium
- If A and B are arbitrary constants, then the differential equation having \(\mathrm{y}=\mathrm{Ae}^{\mathrm{x}}+\mathrm{B} \sin 2 \mathrm{x}\) as its general solution isTS EAMCET 2023 Medium
- The random variable takes the values \(1,2,3\), \(\ldots, m\). If \(P(X=n)=\frac{1}{m}\) to each \(n\), then the variance of \(X\) isTS EAMCET 2013 Hard
- The solution of isTS EAMCET 2021 Easy
- If the mean and variance of a binomial distribution are \(\frac{4}{3}\) and \(\frac{10}{9}\) respectively, then \(\mathrm{P}(\mathrm{X} \geq 6)=\)TS EAMCET 2025 Medium
More PYQs from TS EAMCET
- If \(A, B, C\) are three events of a sample space such that \(P(B)=\frac{3}{2} P(A)\) and \(P(C)=\frac{1}{2} P(B)\) then which of the following is correct?TS EAMCET 2020 Medium
- The bodies of masses \(100 \mathrm{~kg}\) and \(8100 \mathrm{~kg}\) are held at a distance of \(1 \mathrm{~m}\). The gravitational field at a point on the line joining them is zero. The gravitational potential at that point in \(\mathrm{J} / \mathrm{kg}\) is \(\left(G=6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2\right)\)TS EAMCET 2016 Easy
- If \(x\) is so small that \(x^2\) and higher powers of \(x\) may be neglected, then the approximate value of \(\frac{\left(1+\frac{2}{3} x\right)^{-3}(1-15 x)^{-1 / 5}}{(2-3 x)^4}\)TS EAMCET 2015 Hard
- If one of the diameter of the circle \(x^2+y^2-2 x-6 y+6=0\) is a chord to the circle with centre \((2,1)\), then the radius of the bigger circle isTS EAMCET 2019 Medium
- The area (in sq. units) of the portion lying above the \(X\)-axis and enclosed between the curves \(y^2=2 a x-x^2\) and \(y^2=a x\) isTS EAMCET 2020 Medium
- TS EAMCET 2021 Medium