Question

Find the inverse of the given function.

Answer 1

Answer:

The inverse is

$y =\sqrt{\frac{(\frac{x-3}{3}) ^{2}+5}{2}}$

Step-by-step explanation:

$y=3\sqrt{2x^{2} -5} + 3$

To find the inverse of the function interchange the terms that's x becomes y and y becomes x

We have

$x=3\sqrt{2y^{2}-5 }+3$

Now solve for y

Move 3 to the other side of the equation

$3\sqrt{2y^{2}-5 } = x-3$

Divide both sides by 3

We have

$\sqrt{2y^{2}-5 } =\frac{x-3}{3}$

square both sides of the equation to remove the square root

That's

$2y^{2}-5 = (\frac{x-3}{3}) ^{2}$

Move 5 to the other side of the equation

$2y^{2} = (\frac{x-3}{3}) ^{2}+5$

Divide both sides by 2

We have

$y^{2} = \frac{(\frac{x-3}{3}) ^{2}+5}{2}$

Find the square root of both sides

We have the final answer as

$y =\sqrt{\frac{(\frac{x-3}{3}) ^{2}+5}{2}}$

Hope this helps you