en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

f(x)=2^x+x^2

Solution

f (x) = 2^{x} + x^{2}

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Minimum - \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{ln ( 2 )}, 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}, \infty

Solution steps

Domain of

2^{x} + x^{2} : - \infty < x < \infty

Range of

2^{x} + x^{2} : f (x) \geq 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

None

Extreme Points of

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

Minimum

- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{ln ( 2 )}, 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

Graph

Popular Examples

f(x)=sqrt(x)(5-6x+3\sqrt[4]{x})

f(x)=(3log_{10}(x^2-9x-10))-9

f(x)=(1/4)^{-1}

Frequently Asked Questions (FAQ)

What is the f(x)=2^x+x^2 ?
The f(x)=2^x+x^2 is