can anyone help with Inverse Functions and who to brake them down have problems with is!!!
f(x) = 2x2 - 1

Question

across · Answer

Let$$f(x)$$be a bijection such that$$f:\mathbb{R}\to\mathbb{R}.$$The function can then have an inverse, denoted as$$f^{-1}(x),$$such that$$f^{-1}(f(x))=x.$$E.g., to find the inverse of$$f(x)=y=2x^2-1,$$you swap the variables and solve for y:$$x=2y^2-1.$$Can you solve for y?

fools101 · Answer

yes we can use y?

fools101 · Answer

can we?

fools101 · Answer

wow that was confuse I'm still confuse :(

across · Answer

$$x=2y^2-1.$$How can you solve for y? You add 1 to both sides:$$x+1=2y^2,$$then you divide both sides by 2:$$\frac{x+1}{2}=y^2,$$and finally, you take the square root of both sides:$$y=\pm\sqrt{\frac{x+1}{2}}.$$However, note that this is not a function.

fools101 · Answer

f(x) = 2x2 - 1 so i change it to  a Y?

fools101 · Answer

so it would be F(Y) = 2x2-1?

across · Answer

If you have a function$$y=f(x),$$you swap the variables and solve for y:$$x=f(y).$$

fools101 · Answer

oh but i don't  for the Answer it show  this F^-1 for all the Answer but my problem is f(x) = 2x2 - 1 idk who to brake it down

across · Answer

I already did it for you up there.

fools101 · Answer

like this for Example: f(x) = (x - 1)2 - 5 what i did for this one was like 
Y = (x-1)^2 -5

Y = (x-1)^2 - 5

X = (y - 1)^2  -5
 mathml equation = mathml equation

mathml equation

fools101 · Answer

$$\sqrt{X +5} = \sqrt{Y- 1}     \sqrt{X+5}$$ and  X+ 5 is my Answer.

fools101 · Answer

while i know but non of my Answers have nothing to do with y?

across · Answer

Okay, let me work that one out step by step: We have that$$y=(x-1)^{2}-5.$$To find the inverse of this function, we first swap variables:$$x=(y-1)^{2}-5.$$Now that we have swapped variables, we want to solve for y alone. First, we add 5 to both sides:$$x+5=(y-1)^{2}.$$Next, we take the square root of both sides:$$\pm\sqrt{x+5}=y-1.$$Finally, we add 1 to both sides:$$\pm\sqrt{x+5}+1=y.$$Therefore, we see that$$y=\pm\sqrt{x+5}+1,$$and we have found the function's inverse.

fools101 · Answer

Awww know that one but who would this work f(x) = 2x^2 - 1

fools101 · Answer

how*

across · Answer

Again, I did it for you up there...

fools101 · Answer

ohh kk that make no since but thank u Across for trying to help!