Question

If f (x) = startroot one-half x minus 10 endroot 3, which inequality can be used to find the domain of f(x)? startroot one-half x endroot greater-than-or-equal-to 0 one-half x greater-than-or-equal-to 0 one-half x minus 10 greater-than-or-equal-to 0 startroot one-half x minus 10 endroot 3 greater-than-or-equal-to 0

Answer 1

A function assigns values. The inequality one-half x minus 10 greater-than-or-equal-to 0 should be satisfied.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The domain of a function is a set of values for which the equation is satisfied. Since the function has under root values, the value which is under the root should be non-negative so that it does not give a complex number,  therefore,

The inequality $\sqrt{\dfrac12x^2-10}\geq 0$satisfied to find the domain of the function f(x).

Also, we can write that 0.5x²-10≥0 for the value to be positive.

Hence, the inequality one-half x minus 10 greater-than-or-equal-to 0 should be satisfied.

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