Question

select the correct answer.
find the inverse of the given function.
$f(x) = \sqrt3{7x - 4}$
$f^{-1}(x) = \frac{4-x^3}{7}$
$f^{-1}(x) = 7x^3 + 4$
$f^{-1}(x) = -7\sqrt3{x} + 4$
$f^{-1}(x) = \frac{x^3+4}{7}$

Explanation:

Step1: Set $y = f(x)$

$y = \sqrt[3]{7x - 4}$

Step2: Swap $x$ and $y$

$x = \sqrt[3]{7y - 4}$

Step3: Cube both sides

$x^3 = 7y - 4$

Step4: Isolate the term with $y$

$7y = x^3 + 4$

Step5: Solve for $y$

$y = \frac{x^3 + 4}{7}$

Answer:

$f^{-1}(x) = \frac{x^3 + 4}{7}$