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The function f is defined by
[#permalink]
02 Dec 2020, 09:23

Expert Reply

Question Stats:

The function \(f\) is defined by \(f(x)=\sqrt{x^2}\). For which of the following values of x is \(f(x)=x\) ?

Indicate all such values.

A. −10,000

B. −1

C. −.00001

D. 0

E. .00001

F. 10,000

Kudos for the right answer and explanation

Indicate all such values.

A. −10,000

B. −1

C. −.00001

D. 0

E. .00001

F. 10,000

Kudos for the right answer and explanation

Re: The function f is defined by
[#permalink]
02 Jan 2021, 01:38

1

Carcass wrote:

The function \(f\) is defined by \(f(x)=\sqrt{x^2}\). For which of the following values of x is \(f(x)=x\) ?

Indicate all such values.

A. −10,000

B. −1

C. −.00001

D. 0

E. .00001

F. 10,000

Kudos for the right answer and explanation

Indicate all such values.

A. −10,000

B. −1

C. −.00001

D. 0

E. .00001

F. 10,000

Kudos for the right answer and explanation

Any number squared will yield a positive number.

If we check option B: -1 x -1 = 1, so f(-1) = √1 and √1 = 1 , hence f(x) is not equal to x.

In the same way we can eliminate A and C because they are negative.

0 x 0 is 0 and √0 = 0, option D is satisfying the condition.

0.00001 x 0.00001 = 0.0000000001 but √0.0000000001 = 0.00001, so option E is getting satisfied.

Square root of 10000 x 10000 = 10000, option F is also getting satisfied.

Therefore the correct answer options are D, E & F.

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The function f is defined by
[#permalink]
07 Aug 2022, 10:19

1

Given that \(f(x)=\sqrt{x^2}\) and we need to find the value of x for which \(f(x)=x\)

\(f(x)=\sqrt{x^2}\) = x (given)

=> |x| = x (Watch this video to learn about the Basics of Absolute Value)

Now, |x| = x is true only for non negative values of x, as |x| can never be negative

Only non-negative values in the option choices are 0, .00001 and 10,000

So, Answer will be D, E, F.

Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

_________________

\(f(x)=\sqrt{x^2}\) = x (given)

=> |x| = x (Watch this video to learn about the Basics of Absolute Value)

Now, |x| = x is true only for non negative values of x, as |x| can never be negative

Only non-negative values in the option choices are 0, .00001 and 10,000

So, Answer will be D, E, F.

Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

_________________

Ankit

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The Princeton Review Quantitative Directory

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to My YouTube Channel to ENCOURAGE me to Keep Putting Regular Updates!!!

How to Solve :

Prime Numbers || Circles || Equilateral Triangle in a Circle || Arithmetic and Geometric Progression || Divisibility Rules || Absolute Value || Inequalities || Statistics || Functions and Custom Characters || Remainders || LCM and GCD || Stem & Leaf Plot || Box And Whisker Plot

GRE Club Topic Wise Problems

GRE Quant - 2019 Ed

GRE Verbal - 2019 Ed

The Princeton Review Quantitative Directory

The 5 lb. Book of GRE Practice Problems (2nd Ed.) - QUANT

GRE - PowerPrep® The FREE Practice Tests Explained 2019

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