Should I find them?

Algebra Level 4

3 ∣ x ∣ − ∣ 2 − ∣ x ∣ ∣ = 1 \large 3^{|x|}-|2-|x||=1

Find the number of real values of x x that satisfy the above equation.

Notation : ∣ ⋅ ∣ | \cdot | denotes the absolute value function .


The answer is 2.

Akshat Sharda by Akshat Sharda , 21, India

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2 solutions

Sabhrant Sachan
Jul 7, 2016

Consider the intersection of the graphs of y = 3 ∣ x ∣ y= 3^{|x|} and y = 1 + ∣ 2 − ∣ x ∣ ∣ y=1+\left|2-|x| \right|

2 Helpful 0 Interesting 0 Brilliant 0 Confused
J D
Jul 27, 2016

Split the domain into a piece wise function, then see if each piece has a solution using the intermediate value theorem

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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