What is sqrt(x^2+1)>x-1 ?

The solution to sqrt(x^2+1)>x-1 is True for all x

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sqrt(x^2+1)>x-1

x^{2} + 1 > x - 1

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

x^{2} + 1 > x - 1

f (x) > g (x)

then

g (x) < 0 or g (x) \geq 0

For

x - 1 < 0 : x < 1

For

x - 1 \geq 0 : x \geq 1

Combine the intervals

x \geq 1 or x < 1

Merge Overlapping Intervals

True for all x

Verify Solutions:

The solution is

True for all x

x^{2} + 1 \geq 0

x < 5

5 x - 4 + 3 x + 1 < 3

2 x - 1 < x

x - 1 < x^{2} + 1