Calculus

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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= ???

  • Calculus -

    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)

  • Calculus -

    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!

  • Calculus -

    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)

  • Calculus -

    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!

  • Calculus -

    Long story short - I did the hard work, and I didn't think the second part of the question would be that easy, haha.

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