Find the inverse of f(x). (there are two)

Question

Find the inverse of f(x).  (there are two)

haleyelizabeth2017 · Answer

$$f(x)=-4x^2+1$$

haleyelizabeth2017 · Answer

Don't I switch f(x) and x to begin with?

nnesha · Answer

f(x) is same as y  so we can rewrite this as $$\huge\rm y=-4x^2+1$$
to find inverse switch x and y

whpalmer4 · Answer

and solve for $y$

nnesha · Answer

yes right

jdoe0001 · Answer

$\bf f(x)={\color{blue}{  y}}=-4{\color{brown}{  x}}^2+1\qquad inverse\implies {\color{brown}{  x}}=-4{\color{blue}{  y}}^2+1\impliedby f^{-1}(x)$

yes

haleyelizabeth2017 · Answer

I got:

$$y=\sqrt{\frac {x-1}{-4}}$$

nnesha · Answer

hmm $$\huge\rm \color{ReD}{x}=-4\color{blue}{y}^2+1$$     divide by -4 $$\frac{ x-1 }{ -4 } $$ is same as $$\huge\rm \frac{ x }{ -4 } -\frac{ 1 }{ -4 }$$
first divide the sign and then take square root 
and remember when we take square root we should get 2 solutions $$\sqrt{x^2} = \pm x$$

haleyelizabeth2017 · Answer

wait, what? Sorry, you lost me there lol

nnesha · Answer

$$\frac{ x }{ -4 }-\frac{ 1 }{ -4 } = -\frac{ x }{ 4 }+\frac{ 1 }{ 4 }$$  
-1 divided by -4 = positive 1/4

haleyelizabeth2017 · Answer

oh

nnesha · Answer

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