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

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Math Revolution GMAT Instructor
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Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what  [#permalink]

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New post 24 Oct 2018, 00:19
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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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Re: Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what  [#permalink]

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New post 24 Oct 2018, 01:15
MathRevolution 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 \(f(-3)\) ?

\(A. -9\)
\(B. -3\)
\(C. 0\)
\(D. 3\)
\(E. 9\)


Notice that the given polynomial function f(x) contains even exponents of x, i.e, \(x^4\) and \(x^2\). Hence f(x) is an even function.
Therefore f(-x)=f(x)

Hence, f(-3)=f(3)=9.

Ans. (E)
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Re: Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what  [#permalink]

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New post 25 Oct 2018, 23:54
1
=>

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

Therefore, the answer is E.
Answer: E
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Re: Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what &nbs [#permalink] 25 Oct 2018, 23:54
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Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(3)=9, what

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