Question

convert the function y=f(x)=sqrt(x²-5²) on the domain of all real numbers. (a) Derivative of [ln x] - (b) Do you need to verify - or w

Answer 1

The original function involves the square root of a quadratic expression and is not defined for all real numbers. The correct domain consists of real numbers where the expression under the square root is nonnegative. The derivative of ln(x) is 1/x for x > 0.

Step-by-step explanation:

The function provided is y = f(x) = √(x² - 5²) which appears to represent a function that involves the square root of a quadratic equation. However, the function as stated is not clearly defined over the domain of all real numbers because the square root of a negative number is not defined within the real number system. Assuming that this was a typographical error and the student is asking to convert the function y = f(x) = √(x² - 5²) over its domain, this function is only defined for values of x such that x² - 25 ≥ 0. The derivative of ln(x), which is part (a) of the question, is ¹/x, and this derivative exists for all x > 0.