1. Function Notation help!

Given f(x) = √x - 2, find: 3f(4(x-1)) + 5

I cannot get started.

2. Think of f as "doing something" to what's in the bracket.

In this case f means "take the square root and subtract 2".

So look at what you have:

$3f(4(x-1)) + 5$

In the brackets defining the f there's $4(x-1)$.

So do the square root of all that and subtract 2. Then when you done that, multiply the whole thing by 3 and then add 5.

3. kk ill try that and get back to you tomorrow

4. i still cant get it man

can u show me a step by step?

this is how far i get

Given f(x) = √x - 2, find: 3f(4(x-1)) + 5

f(x) = √(4x-4)

Basically I dumbed down the brackets of (4(x-1)) to (4x-4) and put that in for x, but I don't know what to do from there....

5. Originally Posted by quick.on.my.feet
i still cant get it man

can u show me a step by step?

this is how far i get

Given f(x) = √x - 2, find: 3f(4(x-1)) + 5

f(x) = √(4x-4)

Basically I dumbed down the brackets of (4(x-1)) to (4x-4) and put that in for x, but I don't know what to do from there....
$f(4(x - 1)) = \sqrt{4(x - 1)} - 2$.

$3 f(4(x - 1)) = 3 (\sqrt{4(x - 1)} - 2)$.

$3 f(4(x - 1)) + 5 = 3 (\sqrt{4(x - 1)} - 2) + 5$.

Simplify.

6. that's exactly what i did, but idk how to dumb down the square root and stuff.

7. One thing you can do is note that:
$\sqrt {4 (x-1)} = \sqrt 4 \sqrt {x-1} = 2 \sqrt {x-1}$
and then you can tidy up the rest without bothering to do anything else with what's under the square root.

8. ok my teacher explained it to me
I didn't know i had to multiply the WHOLE thing by 3