What is the domain of f(x)=sqrt(-1/2 x^2+2x+3) ?

The domain of f(x)=sqrt(-1/2 x^2+2x+3) is -sqrt(10)+2<= x<= sqrt(10)+2

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domain of f(x)=sqrt(-1/2 x^2+2x+3)

domain

f (x) = - \frac{1}{2} x^{2} + 2 x + 3

- 10 + 2 \leq x \leq 10 + 2

Interval Notation

[- 10 + 2, 10 + 2]

Solution steps

Find non-negative values for radicals:

- 10 + 2 \leq x \leq 10 + 2

The function domain

- 10 + 2 \leq x \leq 10 + 2

What is the domain of f(x)=sqrt(-1/2 x^2+2x+3) ?
The domain of f(x)=sqrt(-1/2 x^2+2x+3) is -sqrt(10)+2<= x<= sqrt(10)+2