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Popular >

f(x)=2^x-x

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 2^{\frac{l n ( \frac{1}{l n ( 2 )} )}{l n ( 2 )}} - \frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}

Y Intercepts : (0, 1)

Asymptotes : Slant y = - x

Extreme Points : Minimum \frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}, 2^{\frac{l n ( \frac{1}{l n ( 2 )} )}{l n ( 2 )}} - \frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : 2^{\frac{l n ( \frac{1}{l n ( 2 )} )}{l n ( 2 )}} - \frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}, \infty

Solution steps

Domain of

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

Range of

2^{x} - x : f (x) \geq 2^{\frac{l n ( \frac{1}{l n ( 2 )} )}{l n ( 2 )}} - \frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}

Axis interception points of

2^{x} - x :

Y Intercepts

: (0, 1)

Asymptotes of

2^{x} - x :

Slant

: y = - x

Extreme Points of

2^{x} - x :

Minimum

\frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}, 2^{\frac{l n ( \frac{1}{l n ( 2 )} )}{l n ( 2 )}} - \frac{ln ( \frac{1}{l n ( 2 )} )}{ln ( 2 )}

Popular Examples

f(x)=(x^2)/(1+2x)

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

f(x)=2|x-2|-3|3+x|

f (x) = 2 ∣ x - 2 ∣ - 3 ∣ 3 + x ∣

y = \frac{e ^{x}}{1 - 2 x}

y=-13/9 x^2+8/3 x+37/10

y = - \frac{13}{9} x^{2} + \frac{8}{3} x + \frac{37}{10}

y=cos((1-e^{2x})/(1+e^{2x)})

y = cos (\frac{1 - e ^{2 x}}{1 + e ^{2 x}})

Frequently Asked Questions (FAQ)

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