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(2r-4 )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=2r-4,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.
(a) 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.
Then, we can write y as a function of u by substituting u back into the original function:
y = 12^u.
So, the composition of two functions would be:
y = (12^u) as the outer exponential function, with u = 19x + 7 as the inner function.
(b) To express the function P = sqrt(10t^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.
Then, we can write P as a function of u by substituting u back into the original function:
P = sqrt(u).
So, the composition of two functions would be:
P = sqrt(u) as the outer root function, with u = 10t^8 + 2 as the inner function.
(c) To express the function w = 3ln(2r - 4) 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 = 2r - 4.
Then, we can write w as a function of u by substituting u back into the original function:
w = 3ln(u).
So, the composition of two functions would be:
w = 3ln(u) as the outer logarithmic function, with u = 2r - 4 as the inner function.