How many common points have $y=|x|$ and $y=|x^2 - 4|$ ?

Answer Choices

Correct answer marked below

Correct

Infinitely many

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

Equation:

y=|x|=|x^2-4|

As both sides are positive, we can square the two sides:

x^2=x^4-8x^2+16

x^4-9x^2+16=0

An equation of degree 4 will have 4 values of x. We can find the values through determinant or factorisation, but that may be beyond GMAT scope. In some cases, we can have same values of x leading to fewer than 4 distinct points. For example,

x^4=16

has only two different values: 2 and -2.…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

What this question tests

What it tests

Your ability to evaluate and compose functions, including unusual defined operations.

Common trap

Applying function operations in the wrong order or ignoring domain restrictions.

How many common points have y=∣x∣y=|x|y=∣x∣ and y=∣x2−4∣y=|x^2 - 4|y=∣x2−4∣?