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Find the domain and range of f(x)=√x^2-7x+12Asked by Biruk getasew
Find the domain and range of f(x)=x^2-5x+6
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The function is a quadratic function, which means that the domain is all real numbers, since the function exists for any value of x.
To find the range, we can use the fact that the vertex of the parabola is at x = -b/2a = 5/2.
Since the coefficient of x^2 is positive, the parabola opens upwards, and the minimum value occurs at the vertex.
Substituting x = 5/2 into the original equation, we get f(5/2) = (5/2)^2 - 5(5/2) + 6 = -1/4.
Therefore, the range of the function is (-1/4, infinity).
To find the range, we can use the fact that the vertex of the parabola is at x = -b/2a = 5/2.
Since the coefficient of x^2 is positive, the parabola opens upwards, and the minimum value occurs at the vertex.
Substituting x = 5/2 into the original equation, we get f(5/2) = (5/2)^2 - 5(5/2) + 6 = -1/4.
Therefore, the range of the function is (-1/4, infinity).
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