KCET · Maths · Functions
If \(f(x)=a x+b\), where \(a\) and \(b\) are integers, \(f(-1)=-5\) and \(f(\beta)=3\), then \(a\) and \(b\) are respectively
- A \(2,-3\)
- B 0,2
- C 2,3
- D \(-3,-1\)
Answer & Solution
Correct Answer
(A) \(2,-3\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=a x+b\), where \(a\) and \(b\) are
integers, \(f(-1)=-5\) and \(f(3)=3\)
We have, \(f(x)=a x+b\)
Put, \(x=-1\) in above equation, we get
\(\begin{aligned} f(-1) & =a(-1)+b \\ -5 & =-a+b\end{aligned}\)
Now, \(f(3)=3\)
\(3=3 a+b\)
From Eqs. (i) and (ii), we get
\(a=2, b=a-5=2-5=-3\)
integers, \(f(-1)=-5\) and \(f(3)=3\)
We have, \(f(x)=a x+b\)
Put, \(x=-1\) in above equation, we get
\(\begin{aligned} f(-1) & =a(-1)+b \\ -5 & =-a+b\end{aligned}\)
Now, \(f(3)=3\)
\(3=3 a+b\)
From Eqs. (i) and (ii), we get
\(a=2, b=a-5=2-5=-3\)
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 the volume of the parallelopiped formed by three non-coplanar vectors \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) is 4 cu units, then \([\mathbf{a} \times \mathbf{b} \mathbf{b} \times \mathbf{c} \mathbf{c} \times \mathbf{a}]\) is equal toKCET 2012 Medium
- \(\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)\) is equal toKCET 2020 Medium
- If \(x-y=1\) is a tangent to the hyperbola \(\frac{x^{2}}{4}-\frac{y^{2}}{3}=1\), then the point of contact isKCET 2012 Medium
- The image of the point \( (1,6,3) \) in the line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) isKCET 2018 Hard
- \(\int_0^{\pi / 2} \frac{\cos x \sin x}{1+\sin x} d x\) is equal toKCET 2022 Hard
- If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are unit vectors such that \(\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\), then angle between \(\mathbf{a}\) and \(\mathbf{b}\) isKCET 2011 Medium
More PYQs from KCET
- Critical Micelle concentration for a soap solution is \( 1.5 \times 10^{-4} \mathrm{~mol} L^{-1} \). Micelle formation is
possible only when the concentration of soap solution in \( \mathrm{mol} L^{-1} \) isKCET 2019 Medium - With respect to resonance structures of \(\text{CO}_3^{2-}\) ion, which of the following statements are correct?
(a) All \(\text{C}-\text{O}\) bonds in \(\text{CO}_3^{2-}\) are equivalent
(b) There are three resonance structures possible for \(\text{CO}_3^{2-}\) ion
(c) The position of carbon and oxygen should change in every resonance structure
(d) The formal charge on carbon atom is \(-2\)KCET 2026 Medium - What is the value of shunt resistance required to convert a galvanometer of resistance \( 100 \Omega \)
into an ammeter of range \( 1 \mathrm{~A} \)?
Given : Full scale deflection of the galvanometer is \( 5 \mathrm{~mA} \).KCET 2014 Medium - Electrical as well as gravitational affects can be thought to be caused by fields. Which of the following is true for an electrical or gravitational field?KCET 2022 Easy
- Which one of the following is not true regarding electromeric effect?KCET 2012 Easy
- \( \int_{0}^{\frac{\pi}{2}} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \) is equal toKCET 2017 Hard