Question

if f(x)= 2x^2+5sqrt(x-2), complete the following statement: The domain for f(x) is all real numbers _____ than or equal to 2. (fill in the blank)

Answer 1

Answer:

Greater.

Step-by-step explanation:

The in the function  $f(x)=2x^2+5\sqrt{x-2}$, the square root term $\sqrt{x-2}$ has to give a real number if $f(x)$ is to be real. This can only happen if $x\geq 2$ because if $x$ then $\sqrt{x-2}$ will give a complex number and therefore $f(x)$ will not be real.

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