Question

Find the domain and range of the function: f(x) = |x| + |1 + x|

Answer 1

Answer:

Dom f(x) = -∞ < x < ∞

Range f(x) ≥ 1

Step-by-step explanation:

To find the domain and range of the function: f(x) = |x| + |1 + x|

as the given function does not having any undefined points ,so domain of function is entire range of real numbers

Dom f(x) = -∞ < x < ∞

For range:

f(x) = |x| + |1 + x|

by putting the values of x or by analysis we can get the function interval as

x < -1 , -1 ≤ x < 0, x ≥ 0

now in each the interval check the function behaviour

1) for interval: x < -1 or -∞ < x < -1

1 < f(x) < ∞

2) for interval :-1 ≤ x < 0: f(x) = 1

3)for interval : 0 < x < ∞ :

1 ≤ f(x) < ∞

now on combined all the values of domain we can find the range of function: f(x) ≥ 1