Help!! I'm doing homework right now and I'm really struggling with it. could anyone walk me though f(x)=3|2x-1|+x find f(-4)

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- anonymous

- schrodinger

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- anonymous

Try simplifying this.
\[3(2x + 1)\]
Can be simplified to
\[5x + 5\]
by multiplying the inside of the brackets by 3.

- anonymous

okay that makes since can you keep explaining? I'm kinda getting it

- anonymous

This makes the sum
\[f(x) = (5x + 5) + x\]
You can simplify it further by removing the '+x' by putting it inside the brackets. That gives you
\[F(x) = 6x + 5\]
Now try removing x from the first side. That'll give you f.
Remember, what ever you do to one side you must do to the other.

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- anonymous

so to get f by itself would I multiply x or 5?

- anonymous

I mean subtract

- anonymous

F(x) is F times X, so you remove the x by dividing both sides by x.

- anonymous

okay so if I do that I get f=6x+4 ? I'm sorry this is so confusing.

- anonymous

Huh?
Ok.
6x divided by x is 6. does that help?

- anonymous

OH so f=6+5?

- anonymous

Yeah.

- anonymous

NO WAIT GOD IT'S A FUNCTION

- anonymous

ERASE EVERYTHING I JUST SAID

- anonymous

GOD I'm SO SORRY

- anonymous

it's okay haha

- anonymous

Right. This is much easier, actually.
Don't actually erase everything, because the simplification still stands
You just need to work out
\[6x + 5\]
if X is -4.

- anonymous

that was my bad I should of told youðŸ˜‚

- anonymous

so would I do 6â€¢-4+5?

- anonymous

No, I was a muppet and completely forgot F(x) means x is input thus function.

- anonymous

Yeah, exactly. For real and proper this time :)

- anonymous

okay so is that all since I found -4's function or is there more?(:

- anonymous

Yup, that's all. For functions, if you need to find f and you have the input, you just substitute the input for x.

- anonymous

thank you so much this makes total since now! you are a life saver

- anonymous

On the plus side, you now know how to solve both\[fx = 3(2x+1) + x\] and \[f(x) 3(2x + 1) +x\] which are for some reason completely different.

- anonymous

No problem! Thank you for forgiving my muppetosity :)

- anonymous

so my answer to this problem is just 6â€¢-4+5

- anonymous

Yeah.

- anonymous

okay thank you again

- anonymous

NO

- anonymous

GOD NOT AGAIN I'M SO STUPID
It doesn't simplify to 5x + 5. It's 6x + 3.
So
\[F(-4) = (6x + 3) + x\]
equals
\[F(-4) = (7 \times -4) +3\]
So F(-4) = -25.
This time I'm pretty sure I'm right, but give me a minute and I'm sure I'll find out I'm counting in the wrong language or something.

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