What is the f(x)=(2e^{x-1}+(2x-1))/(2x-1) ?

The f(x)=(2e^{x-1}+(2x-1))/(2x-1) is

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

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

Domain : x < \frac{1}{2} or x > \frac{1}{2}

Range : f (x) < 1 or f (x) \geq e^{\frac{1}{2}} + 1

X Intercepts : - \frac{2 W _{0} ( \frac{1}{e ^{\frac{1}{2}}} ) - 1}{2}, 0, Y Intercepts : (0, - \frac{2}{e} + 1)

Asymptotes : Vertical x = \frac{1}{2}, Horizontal y = 1

Extreme Points : Minimum (\frac{3}{2}, e^{\frac{1}{2}} + 1)

Interval Notation

Domain : (- \infty, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Range : (- \infty, 1) \cup [e^{\frac{1}{2}} + 1, \infty)

Solution steps

Domain of

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

Range of

\frac{2 e ^{x - 1} + 2 x - 1}{2 x - 1} : f (x) < 1 or f (x) \geq e^{\frac{1}{2}} + 1

Axis interception points of

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

X Intercepts

: - \frac{2 W _{0} ( \frac{1}{e ^{\frac{1}{2}}} ) - 1}{2}, 0,

Y Intercepts

: (0, - \frac{2}{e} + 1)

Asymptotes of

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

Vertical

: x = \frac{1}{2},

Horizontal

: y = 1

Extreme Points of

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

Minimum

(\frac{3}{2}, e^{\frac{1}{2}} + 1)

What is the f(x)=(2e^{x-1}+(2x-1))/(2x-1) ?
The f(x)=(2e^{x-1}+(2x-1))/(2x-1) is