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Algebra - Functions

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Apr 19, 2016 12:36 pm
If x > 0, does f(x²) = [f(x)]² ?

(1)f(x)=√x

(2)x=9
Target question: Does f(x²) = [f(x)]² ?

Statement 1: f(x)=√x
Since we now know what the function looks like, the target question BECOMES . . .
Does √(x²) = (√x)²?
The answer to this question is YES.
If x > 0, then √(x²) definitely equals (√x)²
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x=9
Since we don't know anything about the function f, we cannot answer the target question with certainty.
So statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by OptimusPrep » Thu Apr 21, 2016 7:54 pm
lucas211 wrote: If x>0, does f(x^2) = f(x)^2?

1) F(x)= √x

2) x = 9
Given: x > 0
Required: Is f(x^2) = f(x)^2 ?

Statement 1: f(x)= √x
f(x^2) = √(x^2) = +- x
But we know that x > 0,
Hence
f(x^2) = x

f(x)^2 = (√x)^2
Square of any number will be positive
Hence f(x)^2 = x
Yes, both the values are equal.
Sufficient

Statement 2: x=9
We are just told about the value of x, but do not know anything about the relation between f(x) and x
Hence we cannot calculate the value.
Insufficient

Correct Option: A
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