ShmoopTube

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Here’s your shmoop du jour, brought to you by Real Numbers.

00:06

Seriously – they haven’t had any plastic surgery whatsoever.

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G of x equals the square root of 4 minus x squared.

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For which values of x is the equation true? 

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And here are the potential answers…

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Ok, so the question tells us we’re trying to find the values of x that make this square root function true.

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Well, we know that since g of x involves a radical,

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the only way this equation is true is if the stuff under the radical is non-negative.

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Which…is just a fancy-shmancy way of saying zero or higher.

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For this to happen, x squared can't be greater than 4.

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In other words, x squared must be less than or equal to 4.

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We can automatically eliminate answer choice E as “all real numbers”

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To put this equation another way, x must be equal to or fall between -2 and 2.

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Let’s try a number just to see if this works…

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we’ll go with the ever popular zero. 4 minus 0 squared, or 4 minus 0, is 4.

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And we can take the square root of 4… which equals plus or minus 2...

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so looks like the equation is true for all numbers equal to or between negative 2 and 2.

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And the answer’s C.

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