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Question

Find the number of values of x which satisfy the relation |x4| +|x8| = 4

A

1

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B

2

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C

No solution

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D

Infinite number of x

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Solution

The correct option is D

Infinite number of x


Let f(x) = |x4| + |x8|

We have to find f(x) in the intervals (, 4), [4,8] and [8,].

Let's consider the interval [4,8] first.(you can follow your own order)

4 x 8

|x4|=x4and|x8|= 8 - x

f(x) = x - 4 + 8 - x

= 4

So all the number (rational and irrational) between 4 and 8 satisfy the relation, so the number of solution is infinite.


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