Functions Trap: Algebra Redefined?

In this function trap problem solution , let us solve the given problem and explore how the traps in questions of the functions and functional questions in Algebra lead to traps . It is a challenging problem on inequalities a, discontinuity in functions. Here we have to find the value of x for the discontinuity in the given function. Is it a trap ?. We can find out only after fully solving the problem. This type of problems will be solved here and posted . Let us find out the problem and solve it.

Problem – Is it functions trap?

The problem is given as Multiple Choice Question where we are required to find the correct answer from the given 4 choices. This type of questions are useful for Mathematics Olympiad , CBSE Maths, JEE < Maths. The problem is given in the below image.

Let us solve the above problem of functions and functional equations in algebra step by step.

We also find in this problem of Functions Trap: Why x = 1/49 Is the Answer (Not 1/4!).

Solution of this Functions trap Problem?

Given that,

$\frac{1}{7^{n+1}}<x<\frac{1}{7^n}$

$f(x)=\frac{1}{7^n-3}$ and f(0)=7.

Here f(x) is independent of x and for any given value of n, it is a constant.

Hence f(x) in the given interval it is continuous.

Hence $f(x)=\frac{1}{7^n-3}$ is continuous in the interval $(\frac{1}{7^{n+1}},\frac{1}{7^n})$

At $x=\frac{1}{7^n}$ the right hand and left hand limits can be written as,

$\underset{x\to (\frac{1}{7^n}{)}^{-}}{\mathrm{Lt}}f(x)=\frac{1}{7^n-3}$ and $\underset{x\to (\frac{1}{7^n}{)}^{+}}{\mathrm{Lt}}f(x)=\frac{1}{7^{n-1}-3}$

The values of left hand limit and right hand limits are different at $x=\frac{1}{7^n}$

Hence the discontinuity is at $x=\frac{1}{7^n}$

In the given alternatives, $\frac{1}{49}=\frac{1}{7^2}$

Hence the answer is $\frac{1}{49}$.

The correct answer is b.

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