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Download If , find all values of x such that f(x) = 256
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Transcript
x 2 3 x If f ( x) 4 , find all values of x such that f(x) = 256. Solution: Since f(x)=256, we can plug in 256 for f(x) in the first equation to get. 256 4 x 3 x We need to write both sides of the equation as powers of the same base so we ask: 4 raised to what power is 256? 2 44 4 x 2 3 x Once the bases are the same, we know the exponents must be equal: 4 = x2 + 3x To solve a quadratic equation, we need one side of the equation to be zero, so we subtract 4 from both sides: x2 + 3x – 4 = 0 Factoring: (x + 4)(x – 1) = 0 Setting each factor equal to zero: x + 4 = 0 or x – 1 = 0 x = - 4 or x = 1
