domains: find domain of f(x) = (x - 1)/sqrt(1 - 4x)

[bubblefiz]

I just want to make sure im in the right direction.

Find the domain of f: f(x)= (x-1)/ √1-4x

√1-4x
1-4x>0
-4x>-1
x>-1/4


(x-1)
x-1>0
x>1

so would it be Df={x|x>1}

Note I underlined > for greater than or equal too

Am I on the right track I would appreciate any suggestions

 

[tkhunny]

Re: domains

√1-4x
1-4x>0

Excellent. You saw what you needed to see. Very good.

1-4x>0
-4x>-1
x>-1/4

Not so good.

Your first step just cracks me up. It's not your fault. you teachers probably drilled it into your head this way.

Why would you subtract 1? It's already positive. The other piece is negative. You're just making it uglier. It also confused you later.

1 - 4x > 0
-4x > -1
x < 1/4 <== You missed the sign and forgot to change the inequality.

Try adding 4x, instead.

1 - 4x > 0
1 > 4x
(1/4) > x

Notice how the direction of the inequality took care of itself.

Myth: x must end up on the left or we all will fail math into Eternity.
Busted: Do it the way that makes sense to you AND gets the right answer.