What is the range of f(x)=((x^2+4x-5))/((x^2+x-2)) ?

The range of f(x)=((x^2+4x-5))/((x^2+x-2)) is f(x) 2

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range of f(x)=((x^2+4x-5))/((x^2+x-2))

range

f (x) = \frac{( x ^{2} + 4 x - 5 )}{( x ^{2} + x - 2 )}

f (x) < 1 or 1 < f (x) < 2 or f (x) > 2

Interval Notation

(- \infty, 1) \cup (1, 2) \cup (2, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{x ^{2} + 4 x - 5}{x ^{2} + x - 2} : x < - 2 or - 2 < x < 1 or x > 1

Simplify

\frac{x ^{2} + 4 x - 5}{x ^{2} + x - 2} : \frac{x + 5}{x + 2}

Extreme Points of

\frac{x + 5}{x + 2} :

None

Find the range for the interval

- \infty < x < - 2 : - \infty < f (x) < 1

Find the range for the interval

- 2 < x < 1 : 2 < f (x) < \infty

Find the range for the interval

1 < x < \infty : 1 < f (x) < 2

Combine the ranges of all domain intervals to obtain the function range

f (x) < 1 or f (x) > 2 or 1 < f (x) < 2

f (x) < 1 or 1 < f (x) < 2 or f (x) > 2

- x^{2} + 4 x

f (x) = \frac{7 - 5 x}{5 x + 2}

f (x) = \frac{5 x + 2}{x - 3}

f (x) = 9.46

What is the range of f(x)=((x^2+4x-5))/((x^2+x-2)) ?
The range of f(x)=((x^2+4x-5))/((x^2+x-2)) is f(x)<1\lor 1<f(x)<2\lor f(x)>2