## anonymous one year ago 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)

1. anonymous

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

2. anonymous

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

3. 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.

4. anonymous

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

5. anonymous

I mean subtract

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

OH so f=6+5?

10. anonymous

Yeah.

11. anonymous

NO WAIT GOD IT'S A FUNCTION

12. anonymous

ERASE EVERYTHING I JUST SAID

13. anonymous

GOD I'm SO SORRY

14. anonymous

it's okay haha

15. 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.

16. anonymous

that was my bad I should of told you😂

17. anonymous

so would I do 6•-4+5?

18. anonymous

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

19. anonymous

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

20. anonymous

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

21. 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.

22. anonymous

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

23. 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.

24. anonymous

No problem! Thank you for forgiving my muppetosity :)

25. anonymous

so my answer to this problem is just 6•-4+5

26. anonymous

Yeah.

27. anonymous

okay thank you again

28. anonymous

NO

29. 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.