Calculus
posted by Jessie on .
In order to express the function
y=12^19x+7 as a composition of two functions the outer of which is an exponential function,we would let
u be equal to the inner function,
u=19x+7,
and then write y as a function of u, as follows: y= ???
.
(b) In order to express the function
P=sqrt10t^8+2,as a composition of two functions the outer of which is a root function, we would let u be equal to the inner function, u=10t^8+2, and then write P as a function of u, as follows:
P=???
.
(c) In order to express the function w=3ln(2r4 )as a composition of two functions the outer of which is a logarithmic function, we would let
u be equal to the inner function,
u=2r4,and then write w as a function of u, as follows: w= ???

a) man, they already did have the work. Substitute u=19x+7, and you have
y(u)=12^u
b) P(u)=√u
c) w(u) = ln(u) 
I actually figured out what u was equal to in each of the problems. I just wasn't sure how to answer the rest of the question. But thank you!

As far as I can tell, there is no rest of the question. Each parts asks how to write y,p,w as a function of u.
What is it that still bothers you? If
u(x) = 19x+7
v(x) = 12^x
y(x) = (u◦v)(x) 
Oh, no no. I was able to figure it out based on what you showed me.
You were just surprised that each problem already had the work, and I was simply saying that I was able to figure that part of the question out.
I just wasn't sure how to write the equations as a function of u.
Thank you for your help. I understand it now! 
Long story short  I did the hard work, and I didn't think the second part of the question would be that easy, haha.