Question

What is the inverse of the given function? y=7x^2-3

Answer 1

to find the invers of y=something
1. switch x and y
2. solve for y
3. replace y with f⁻¹(x)

so
y=7x²-3
switch  x and y
x=7y²-3
solve for y
add 3
x+3=7y²
$\frac{x+3}{7} =y^2$
$\sqrt{\frac{x+3}{7}} =y$
$f^{-1}(x)= \sqrt{\frac{x+3}{7}}$
rationalizing denomenator
$f^{-1}(x)= \frac{\sqrt{7(x+3)}}{7}$

Answer 2

The inverse of the function is

$y = \sqrt{ \frac{x + 3}{7} }$

Given the equation, y = 7x²-3

First, we need to swap the given variables

x = 7y² - 3

Add 3 to both sides

x+3 = 7y²-3+3

x+3 = 7y²

Divide both sides by 7

(x+3)/7 = 7y²/7

(x+3)/7 = y²

Take the square root of both sides

$y = \sqrt{ \frac{x + 3}{7} }$

Hence the inverse of the function is

$y = \sqrt{ \frac{x + 3}{7} }$

Learn more here: brainly.com/question/231445