Describe the domain and range of the function:

Question

F(x) = - Sq.rt.of.x+1.?

Answer 1

The function f(x) = - √(x + 1)

Index of the function is 2.

2 is even number.

x + 1 ≥ 0

x ≥ - 1

Domain set is { x ∈ R : x ≥ - 1}

Range set is the corresponding y values of the function for different values of x.

The negative sign in front of the radical in this function.

Since for all non negative real numbers of x , the function is ≤ 0.

For example the first domain value is - 1, then y = -(x + 1)^1/2  = -(- 1 + 1)^1/2 = 0, so the range value starting with 0.

So, the range of the function is always less than or equal to 0.

Range set is{ y ∈ R : y ≤ 0}.