Question

Determine the equation of the inverse of y=7x^(3)+2

Answer 1

The inverse of the equation would be solving for x, so the answer is..
the square root of y-2 with 3 as the index, and the whole equation divided by 7 the equaled to x.

$\sqrt[3]{y-2}/7 = X$

Answer 2

Answer:

$f^{-1}(x)=\sqrt[3]{\frac{1}{7}(x-2)}$

Step-by-step explanation:

The given equation is $y=7x^3+2$

For finding inverse of this function, we apply below steps:-

Step 1

Interchange x and y

$x=7y^3+2$

Step 2

Solve the equation for y

For this, subtract 2 to both sides of the equation

$x-2=7y^3$

Divide both sides by 7

$y^3=\frac{1}{7}(x-2)$

Take cube root both sides,

$y=\sqrt[3]{\frac{1}{7}(x-2)}$

Step 3

Replace y with $f^{-1}(x)$

Therefore, the inverse function is

$f^{-1}(x)=\sqrt[3]{\frac{1}{7}(x-2)}$