[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
Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f(
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- Max@Math Revolution
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$$f\left( x \right) = a \cdot {x^4} + b \cdot {x^2} + 1\,\,\,\,\,\,\left( {a,b\,\,{\rm{conts}}} \right)$$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
$$? = f\left( { - 3} \right) = a \cdot {\left( { - 3} \right)^4} + b \cdot {\left( { - 3} \right)^2} + 1 = a \cdot {3^4} + b \cdot {3^2} + 1$$
$$9 = f\left( 3 \right) = a \cdot {3^4} + b \cdot {3^2} + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9$$
This solution follows the notations and rationale taught in the GMATH method.
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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.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
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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- Max@Math Revolution
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=>
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
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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