F(x) = 5x^2 + 2, find the inverse

Question

asked May 28, 2021 113k views

1 Answer

Ranty · Answer 1 · 2021-06-03T01:05:26+0000

Hey there! :)

Answer:

f^(-1)(x) = ±
$\sqrt{(1)/(5)(x-2) }$

Explanation:

Given:

f(x) = 5x² + 2

Switch the x and y variables in the equation:

x = 5y² + 2

Subtract 2 from both sides:

x - 2 = 5y²

Divide 5 from both sides:

(1)/(5)(x-2) = y^(2)

Square root both sides:

y = ±
$\sqrt{(1)/(5)(x-2) }$

**Make sure to add a ± sign when finding the inverse of a parabolic function.

Therefore, the inverse of this function is:

f^(-1)(x) = ±
$\sqrt{(1)/(5)(x-2) }$