Learn Relations and Functions Problems and crack CAT Quantitative Aptitude

CAT has been giving difficult problems from this topic. A deep understanding of functions is required to solve such problems. We begin with a simple example to show you how to tackle these problems.

Example:

[1] 16

[2] 18

[3] 20

[4] 22

Solution:

Therefore, the correct option is [2].

Example:

[1]  8x10³

[2]  202x10³

[3]  8x202x10³

[4] None of these

Solution:

Therefore, the correct option is [4].

Example:
In which interval must the number ‘m’ vary, so that both roots of the equation x²-2mx+m²-1=0  lie between -2 and 4?

[1] -2<m<5

[2] -3<m<1

[3] -1<m<3

[4]  -5<m<-2

Solution:
The function here is defined by the equation: x²-2mx+m²-1=0

Or the equation can be rewritten as: x²-(2m)x+(m²-1)=0; a=1, b=-2m, c=(m²-1)

Roots if the equation are:

For roots to lie between -2 and 4, we can say that -2<x₁ and x₂ < 4

                                                         Where x_{1 and} x_{2 are the roots}

Also, x₁ = m+1 and x₂ = m-1

Therefore -3 <m<3 and -1 <m<5

Therefore, the region where both the roots will lie between -2 and 4 will be  -1 <m<3 .
Therefore, option [3] is the correct answer.
After understanding the topic well, strat practicing problems on Relations and Functions.