Answer:
The inverse is
[tex]y =\sqrt{\frac{(\frac{x-3}{3}) ^{2}+5}{2}}[/tex]
Step-by-step explanation:
[tex]y=3\sqrt{2x^{2} -5} + 3[/tex]
To find the inverse of the function interchange the terms that's x becomes y and y becomes x
We have
[tex]x=3\sqrt{2y^{2}-5 }+3[/tex]
Now solve for y
Move 3 to the other side of the equation
[tex]3\sqrt{2y^{2}-5 } = x-3[/tex]
Divide both sides by 3
We have
[tex]\sqrt{2y^{2}-5 } =\frac{x-3}{3}[/tex]
square both sides of the equation to remove the square root
That's
[tex]2y^{2}-5 = (\frac{x-3}{3}) ^{2}[/tex]
Move 5 to the other side of the equation
[tex]2y^{2} = (\frac{x-3}{3}) ^{2}+5[/tex]
Divide both sides by 2
We have
[tex]y^{2} = \frac{(\frac{x-3}{3}) ^{2}+5}{2}[/tex]
Find the square root of both sides
We have the final answer as
[tex]y =\sqrt{\frac{(\frac{x-3}{3}) ^{2}+5}{2}}[/tex]
Hope this helps you
