What is the range of e^{sqrt(x+x^2)} ?

The range of e^{sqrt(x+x^2)} is f(x)>= 1

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range of e^{sqrt(x+x^2)}

range

e^{x + x^{2}}

f (x) \geq 1

Interval Notation

[1, \infty)

Solution steps

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

Domain of

e^{x + x^{2}} : x \leq - 1 or x \geq 0

Extreme Points of

e^{x + x^{2}} :

Minimum

(- 1, 1),

Minimum

(0, 1)

Find the range for the interval

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

Find the range for the interval

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

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

f (x) \geq 1 or f (x) \geq 1

f (x) \geq 1

\frac{1}{11 - t}

y = x - \frac{1}{x}

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

f (x) = - 2 tan (2 x)

f (x) = x