Question

Find the domain of the expression 192x^(-7) + 11x^(14/3).

A) x ≠ 0
B) x > 0
C) x < 0
D) All real numbers

Answer 1

The domain for the expression 192x^(-7) + 11x^(14/3) allows both positive and negative values of x, excluding zero. Therefore, option A: x ≠ 0 is the correct domain.

Step-by-step explanation:

The domain of an expression is the set of all possible values of the variable for which the expression is defined. Looking at the expression 192x^(-7) + 11x^(14/3), we note that the term with the negative exponent, x^(-7), implies that x cannot be zero because any number raised to a negative exponent results in the reciprocal of that number to the positive exponent, which is not defined for zero. However, the term with the exponent 14/3 does not raise any issue with x being negative. Hence, the domain of the expression is x ≠ 0, which corresponds to option A: x ≠ 0. No restrictions on the sign of x are given by the second term, so both positive and negative values, except zero, are allowed.