Give two different decompositions of the following functions into two new functions, u and v, where v is the inside function and π’(π₯) β π₯ and π£(π₯) β π₯. Verify that π(π₯) = π’(π£(π₯)) in each case.
+130518 a.
Let u(x) = β x
Let v (x) = 1 - 4ex
Then u ( v(x) ) means that we are subbing v into the "x" in u = β[ 1 - 4ex ] = f(x)
b. This one is a little tricky .....
Let u(x) = 1 + x
______
2 + x
Let v (x) = x^2
1 + x^2
So... u(v (x)) = _________ = f(x)
2 + x^2
c.
Let u(x) = ln (x)
Let v(x) = 2 - 1/x
Then u (v(x)) = ln ( 2 - 1/x) = f(x)
