Question

If f(x)=2(x)^2 + 5 square root (x-2), complete the following statement

The domain for f(x) is all real numbers _____ than or equal to 2.

Answer 1

The domain for f(x) is all real numbers greater than or equal to 2.

Explanation:

Given function:

`f(x)=2x^2+5 √(x-2)`

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken:

`\implies x-2\geq 0`

Therefore:

`\implies x-2+2\geq 0+2`

`\implies x\geq 2`

Therefore, the domain of the given function is greater than or equal to 2.

Answer 2

Greater.

Explanation:

The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.

Thus, the domain for f(x) is all real numbers greater than or equal to 2.