Finding function given new input

[zolton5971]

The function f is defined by f(x)=x^2+5

Find f(3z)

How do I find f(3z)

 

[MarkFL]

Everywhere in the definition of $f(x)$, where you see an $x$, replace it with a $3z$, and then simplify as needed. What do you find?

 

[zolton5971]

f(3z)=5

I'm not sure I not very good at this.

 

[MarkFL]

We are given the definition:

\(\displaystyle f(x)=x^2+5\)

Notice that in the definition, we are told to take the input, square it, and then add 5. So, say the input is $4u$, then we need to square that, which is $(4u)^2$, and then add 5, so that we have $(4u)^2+5$. Hence:

\(\displaystyle f(4u)=(4u)^2+5=4^2u^2+5=16u^2+5\)

Can you now find $f(3z)$?

 

[zolton5971]

f(3z)=3x^2+5= 9z^2+5 is that close?

 

[MarkFL]

f(3z)=3x^2+5= 9z^2+5 is that close?

You have the right end result, but what you want to write is:

\(\displaystyle f(3z)=(3z)^2+5=9z^2+5\)

 

[zolton5971]

Ok thanks!

 

[MarkFL]

I have again moved a new question of yours into a new thread. Please don't tag a new question onto an existing thread, as this can cause threads to become convoluted and hard to follow. Also, your new question will be seen by more people if you begin a new thread for it. :D