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Popular >

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

Solution

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

Solution

Domain : x \leq - 1 or x \geq 1

Range : - 1 \leq f (x) < 0 or f (x) \geq 1

Intercepts : None

Asymptotes : Horizontal y = 0, Slant y = 2 x

Extreme Points : Minimum (- 1, - 1), Minimum (1, 1)

+1

Interval Notation

Domain : (- \infty, - 1] \cup [1, \infty)

Range : [- 1, 0) \cup [1, \infty)

Solution steps

Domain of

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

Range of

x + x^{2} - 1 : - 1 \leq f (x) < 0 or f (x) \geq 1

Axis interception points of

x + x^{2} - 1 :

None

Asymptotes of

x + x^{2} - 1 :

Horizontal

: y = 0,

Slant

: y = 2 x

Extreme Points of

x + x^{2} - 1 :

Minimum

(- 1, - 1),

Minimum

(1, 1)

Popular Examples

intercepts of-x,x<0 intercepts

- x, x < 0

extreme f(y_{=3x^2-8x+5})=y_{=3x^2-8x+5}(x)extreme points

f (y_{= 3 x^{2} - 8 x + 5}) = y_{= 3 x^{2} - 8 x + 5} (x)

f (x) = 4 - 3^{x + 2}

f(x)=3x^4-4x^3-12x^2-1

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} - 1

f (x) = 3 cos (x) + 1

Frequently Asked Questions (FAQ)

What is the f(x)=x+sqrt(x^2-1) ?
The f(x)=x+sqrt(x^2-1) is