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Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(

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by Max@Math Revolution » Wed Oct 24, 2018 12:09 am

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[Math Revolution GMAT math practice question]

Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what is the value of f(-3) ?

A. -9
B. -3
C. 0
D. 3
E. 9
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by fskilnik@GMATH » Wed Oct 24, 2018 2:42 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what is the value of f(-3) ?

A. -9
B. -3
C. 0
D. 3
E. 9
$$f\left( x \right) = a \cdot {x^4} + b \cdot {x^2} + 1\,\,\,\,\,\,\left( {a,b\,\,{\rm{conts}}} \right)$$
$$? = f\left( { - 3} \right) = a \cdot {\left( { - 3} \right)^4} + b \cdot {\left( { - 3} \right)^2} + 1 = a \cdot {3^4} + b \cdot {3^2} + 1$$
$$9 = f\left( 3 \right) = a \cdot {3^4} + b \cdot {3^2} + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9$$

This solution follows the notations and rationale taught in the GMATH method.

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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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by Scott@TargetTestPrep » Thu Oct 25, 2018 4:57 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what is the value of f(-3) ?

A. -9
B. -3
C. 0
D. 3
E. 9
The notation f(3) = 9 means that when x = 3, then y = 9. We are asked to find the value of the function when x = -3.

Before you try to plug -3 into the function ax^4+bx^2+1 and then try to do the lengthy and confusing arithmetic, notice that 3^4 equals (-3)^4, and 3^2 equals (-3)^2. So, no matter if x = 3 OR if x = -3, the answer to the function will be the same for f(3) and for f(-3), since the exponents are even numbers. Thus, f(3) = f(-3) = 9. No arithmetic is necessary!.

Answer: E

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by Max@Math Revolution » Thu Oct 25, 2018 11:45 pm
=>

f(3) =a(3)^4 + b(3)^2 + 1 = 81a + 9b + 1 = 9
f(-3) =a(-3)^4 + b(-3)^2 + 1 = 81a + 9b + 1 = f(3) = 9

Therefore, the answer is E.
Answer: E
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