What is the range of f(x)=-4/(x^2-3x+6) ?

The range of f(x)=-4/(x^2-3x+6) is -16/15 <= f(x)<0

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range of f(x)=-4/(x^2-3x+6)

range

f (x) = - \frac{4}{x ^{2} - 3 x + 6}

- \frac{16}{15} \leq f (x) < 0

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

- \frac{4}{x ^{2} - 3 x + 6}

Inverse of

- \frac{4}{x ^{2} - 3 x + 6} : \frac{3 x + - 15 x ^{2} - 16 x}{2 x}, \frac{3 x - - 15 x ^{2} - 16 x}{2 x}

\frac{3 x + - 15 x ^{2} - 16 x}{2 x}, \frac{3 x - - 15 x ^{2} - 16 x}{2 x}

Find the domain of each inverse function

Domain of

\frac{3 x + - 15 x ^{2} - 16 x}{2 x} : - \frac{16}{15} \leq x < 0

Domain of

\frac{3 x - - 15 x ^{2} - 16 x}{2 x} : - \frac{16}{15} \leq x < 0

Combine the intervals

- \frac{16}{15} \leq f (x) < 0

3 x + 6 y = 5, at

y = 3 - 5 x

(2, 3), (1, 0)

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

f (x) = 4 + 3 x - x^{2}

What is the range of f(x)=-4/(x^2-3x+6) ?
The range of f(x)=-4/(x^2-3x+6) is -16/15 <= f(x)<0