Can someone help me please?
The functions u and w are defined as follows.
u(x)=2x+2
w(x)=-3x+4
Find the value of u(w(−5))

- teller

- chestercat

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- anonymous

Plug -5 into the equation for W, and then take whatever value you get from that and plug it into U. Does that make sense?

- teller

So it would first look like this ? u(5)=2(5)+2

- teller

I got u=12/5

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- teller

Not sure if that's correct or not.

- anonymous

No. So what you have here is a composite function. Whenever you have a composite function, you always solve the function that's next to X first and work your way outward. So for example, if we have f(g(x)), we solve g(x) first, and then we solve f(x) with the number that we got from g(x).

- teller

I'm confused..

- anonymous

Plug -5 into W and tell me what you get

- teller

- 11/5

- anonymous

So -3(-5)+4 is -11/5?
\[W(-5)=-3(-5)+4\]

- teller

oh no -19/5

- anonymous

The (-5) next do the W is not a specifically part of the equation. Whenever we have a function, let's say, F(x), we are saying that we have a function that is related in terms of x. Basically that further means that all of our variables in the equation are going to be in terms of X.
For example, F(x)=x^2
or F(y)=y^2. It's not part of the equation, but it's a statement that helps clarify what variable our equation will use.

- teller

I'm sorry I'm just confused now.....

- teller

That confused me even more sorry....

- anonymous

You're are dividing by -5 when you shouldn't be.
It's not -5*W=-3*-5+4

- teller

I'm not dividing I placed the equation like you wrote into the calculator and that's what I got...

- anonymous

Yes you are. \[W(-5)=-3(-5)+4=19\]
You said `-19/5` which is dividing by a -5.

- teller

That's what I got when I placed it into the calculator... I placed the exact same problem you did what calculator are you using because I'm using mathway,,,

- anonymous

That is because Mathway is interpreting it as "W times -5" and that's not what the question is asking you. It's asking you to evaluate the equation at -5.

- teller

So what do I do then would the final answer be 53? Or -53

- anonymous

\[W(-5)=-3(-5)+4=19\]
\[U(19)=2(19)+2=40\]

- teller

so it would be 40?

- anonymous

Yes :)

- teller

Thank you just math isn't my strongest subject just doesn't stick with me and my teacher knows this but yet she doesn't give a flying f about what happens .She just tells us to do it on our own and expect us to grasp it without lessons or even videos really.

- anonymous

I can understand that frustration. Even professors do that in college and it really bothers me. I would recommend visiting her before or after class and see if she's willing to help. Sometimes teachers won't do much in class, but if you go to see them one-on-one and ask them for help, they'll be happy to. If she says she doesn't want to help you, then I would suggest going to administration or the principal to speak about it. And then find another math teacher before/after school to help you in the meantime.

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