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Mathematics
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What is the range of the function f ( x ) = ( x 1 ) 2 + 17 f(x)=(x-1)^(2)+17 ?
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The given function is f ( x ) = ( x 1 ) 2 + 17 f(x)=(x-1)^(2)+17.
We can find the range of the function by finding the minimum value of f ( x ) f(x) and determining if there are any restrictions on the output values.
Notice that ( x 1 ) 2 (x-1)^(2) is always nonnegative and equals 0 only when x = 1 x=1. Therefore, the minimum value of f ( x ) f(x) occurs when x = 1 x=1 and is equal to f ( 1 ) = 17 f(1)=17.
Since ( x 1 ) 2 (x-1)^(2) can be any nonnegative number, f ( x ) f(x) can take on any value greater than or equal to 17. Therefore, the range of the function is [ 17 , ) [17,oo).
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