Need help with a couple, also please correct me if i'm wrong

3. x=3y+2

-2 from both sides= x-2=3y

(3)x-2(3)=(3)3y=

y=3x-6

4. x=2/3y-5

+5 both sides

x+5=2/3y

(3/2)x+(3/2)5=(3/2)2/3y=

y=3/2x+7.5

5. x=y^2+8

-8 from both sides= x-8=y^2 (not sure what comes next) is it x-8^2=(y^2)^2 ???

6. x=(y+3)^2

Not sure what to do next for this one but I tried a little bit: x^2=((y+3)^2)^2=x^2=y+3 I don't know >.<

RainbowPanda
Aug 21, 2018

#1**+2 **

3. f(x) = 3x + 2

Here's the way I learned it..... for f(x), write "y".... get x by itself... "swap" x and y

and for "y" write f^{-1}(x) [this notation represents the inverse ]

So we have

y = 3x+ 2

y - 2 = 3x

[y - 2] / 3 = x "swap" x and y

[x - 2 ] / 3 = y

[x -2 ] / 3 = f^{-1}(x)

BTW....swapping x and y like you did in your first step is OK, too.....!!

#4 looks good...!!!

Here's the last two

f(x) = x^2 + 8

y = x^2 + 8

y - 8 = x^2 take both roots

±√ [y -8] = x swap x and y

±√[ x - 8 ] = y

±√[x - 8] = f^{-1}(x)

f(x) = (x + 3)^2

y = (x + 3)^2 take both roots

±√y = x + 3

±√y - 3 = x swap x and y

±√x - 3 = y

±√x - 3 = f^{-1}(x)

CPhill
Aug 21, 2018

#2**+2 **

Thank you, that's not quite how I learned it but maybe i'll get used to it being that way...

RainbowPanda
Aug 21, 2018