If the domain of a function f is x and the domain of a function g is x, then the domain of the sum of the function f+g is ______

Question

If the domain of a function f is x and the domain of a function g is -2≤x≤5, then the domain of the sum of the function f+g is ______

Answer 1

-2 ≤ x ≤ 6

Explanation:

For function f:

x - 7 ≤ 0 and x ≥ 0

For function g:

x + 2 ≥ 0 and x - 5 ≤ 0

The sum of the f + g:

x - 7 + x - 5 ≤ 0

2x - 12 ≤ 0

2x ≤ 12

∴ x ≤ 6

Also, x + 2 ≥ 0

x ≥ -2

Hence, -2 ≤ x ≤ 6