What is the range of f(x)= 2/(x+1)*sqrt(1-x) ?

The range of f(x)= 2/(x+1)*sqrt(1-x) is -infinity <f(x)<infinity

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range of f(x)= 2/(x+1)*sqrt(1-x)

range

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

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

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

Domain of

\frac{2}{x + 1} \cdot 1 - x : x < - 1 or - 1 < x \leq 1

Simplify

\frac{2}{x + 1} \cdot 1 - x : \frac{2 - x + 1}{x + 1}

Extreme Points of

\frac{2 1 - x}{x + 1} :

Minimum

(1, 0)

Find the range for the interval

- \infty < x < - 1 : - \infty < f (x) < 0

Find the range for the interval

- 1 < x \leq 1 : 0 \leq f (x) < \infty

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

f (x) < 0 or f (x) \geq 0

- \infty < f (x) < \infty

\frac{2 x ^{2} - 3 x - 9}{x}

m < 6

f (x) = ln (x + 7) - ln (3) + 1

f (x) = (x + 1) (x - 2)

x^{3} - 12

What is the range of f(x)= 2/(x+1)*sqrt(1-x) ?
The range of f(x)= 2/(x+1)*sqrt(1-x) is -infinity <f(x)<infinity