(a) In order to express the function y = 1010 x + 4, 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 = ,
and then write y as a function of u, as follows: y = .
(b) In order to express the function P = √{ 18 t9 + 3 }, 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 = ,
and then write P as a function of u, as follows: P = .
(c) In order to express the function w = 6 ln( 1 r− 5 ) 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 = ,
and then write w as a function of u, as follows: w = .
What is the actual question please?
(a) To express the function y = 1010x + 4 as a composition of two functions, where the outer function is an exponential function, we can let u be equal to the inner function, u = 1010x, and then write y as a function of u.
Let's define the inner function as g(x) = 1010x.
The exponential function that could be the outer function is h(u) = 2^u (assuming base 2 for simplicity).
So, we can express y in terms of u and write it as follows:
y = h(g(x)) = h(u) = 2^u
Therefore, y = 2^(1010x) + 4 is the expression of y as a composition of two functions, where the outer function is an exponential function.
(b) To express the function P = √(18t^9 + 3) as a composition of two functions, where the outer function is a root function, we can let u be equal to the inner function, u = 18t^9 + 3, and then write P as a function of u.
Let's define the inner function as g(t) = 18t^9 + 3.
The root function that could be the outer function is h(u) = √u.
So, we can express P in terms of u and write it as follows:
P = h(g(t)) = h(u) = √u
Therefore, P = √(18t^9 + 3) is the expression of P as a composition of two functions, where the outer function is a root function.
(c) To express the function w = 6ln(1/(r - 5)) as a composition of two functions, where the outer function is a logarithmic function, we can let u be equal to the inner function, u = 1/(r - 5), and then write w as a function of u.
Let's define the inner function as g(r) = 1/(r - 5).
The logarithmic function that could be the outer function is h(u) = ln(u).
So, we can express w in terms of u and write it as follows:
w = h(g(r)) = h(u) = ln(u)
Therefore, w = ln(1/(r - 5)) is the expression of w as a composition of two functions, where the outer function is a logarithmic function.