Question

choose the function that expresses the relationship $15x + 4y^3 = 4$ as a function, $y = f(x)$, if possible.$circ f(x) = sqrt{\frac{4 - 15x}{4}}, -sqrt{\frac{4 - 15x}{4}}LXB0circ f(x) = \frac{4 - 15x}{4}$question help: post to forumcalculator

Explanation:

Step1: Isolate the $y^3$ term

Subtract $15x$ from both sides:
$4y^3 = 4 - 15x$

Step2: Solve for $y^3$

Divide both sides by 4:
$y^3 = \frac{4 - 15x}{4}$

Step3: Solve for $y$

Take the cube root of both sides:
$y = \sqrt[3]{\frac{4 - 15x}{4}}$
For cube roots, every real input has exactly one real output, so this defines a function.

Answer:

$f(x) = \sqrt[3]{\frac{4 - 15x}{4}}$