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Question 532379: If f(x)=x^2-3 and f(a)=46, what is the value of a? Explain.
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! The only tricky thing here is to understand what is meant by f(a) = ?
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This is basically just solving the quadratic equation.
Given:
f(x) = x^2 - 3
f(a) = 46
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In this case, f(a) means solving the f(x) equation as if a = x.
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So, f(x) = f(a)
x^2 - 3 = 46
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The easiest way to solve quadratic equations is to rearrange them (using the rules of algebra) so that the equation is set = 0
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Therefore, subtract 46 from both sides and simplify:
x^2 - 3 - 46 = 46 - 46
x^2 - 49 = 0
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Factor the quadratic equation:
x^2 - 49 = 0 is factored to become:
(x + 7)(x - 7) = 0
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Solving for x to satisfy the factored quadratic equation:
x = 7, or -7
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So, when f(a) = 46, a = 7 or -7
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check the work:
(7)^2 - 3 = 46
49 - 3 = 46
46 = 46 checks
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Note: if we substitute -7 into the function, we get the same answer.
a = 7, -7
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cheers,
Lee
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