Question

Let f(x) = E%7B%20-%201%7D%20%28x%29" id="TexFormula1" title=" \sqrt[3]{11x - 3 \:} determine \: {f}^{ - 1} (x)" alt=" \sqrt[3]{11x - 3 \:} determine \: {f}^{ - 1} (x)" align="absmiddle" class="latex-formula">? here ​

Answer 1

Step-by-step explanation:

Set up f(x).

$\sqrt[3]{11x - 3} = f(x)$

Replace f(x) with y

$\sqrt[3]{11x - 3} = y$

Swap x and y

$\sqrt[3]{11y - 3} = x$

Solve for y

Cube both sides

$11y - 3 = {x}^{3}$

Add 3 to both sides

$11y = {x}^{3} + 3$

Divide both sides by 11

$y = \frac{x {}^{3} + 3 }{11}$

so

$f {}^{ - 1} (x )= \frac{ {x}^{3} + 3}{11}$