Question

What are the x and y intercepts of `y = 2x -sqrt(x^2 + 1)`?

Answer 1

x intercept `->x = sqrt(3)/3`
y intercept`->y = -1`

Explanation:

x intercepts:

These occur where `y = 0`:

`0 = 2x - sqrt(x^2 + 1)`

`sqrt(x^2 + 1) = 2x`

`(sqrt(x^2 + 1))^2 = (2x)^2`

`x^2 + 1 = 4x^2`

`1 = 3x^2`

`1/3 = x^2`

`x = +-1/sqrt(3) = +-sqrt(3)/3`

However, since we're dealing with a function that is in part radical, there can be no negative x-intercept, hence the only x intercept will be `x = sqrt(3)/3`.

y intercepts:

These occur where `x = 0`:

`y = 2(0) - (0^2 + 1)^(1/2)`

`y = 0 - sqrt(1)`

`y = -1`

Hopefully this helps!