Question

How to find restrictions for x??
3. F(x)=2 sqrt x-4

Answer 1

1. none
2. none
3. x ≥ 4

Explanation:

The restrictions placed on the independent variable in a function are those necessary to ensure that the function is defined for all allowed values of that variable.

In the graphs of problems 1) and 2), we see that the functions are defined for all values of x, so there are no restrictions.

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3. For the function ...

`f(x)=2√(x-4)`

the value under the radical cannot be negative. The square root function is not defined for negative values, so the restriction is ...

x -4 ≥ 0

x ≥ 4 . . . . . . . add 4 to both sides of the inequality