Given the functions :?

Question

f( g (h (x))) = sqrt(e^3x+1) +2. Find functions for h(x), g(x), f(x). Can anybody please go through the whole process. I did such kind of problems way too back.

Thanks

Answer 1

Think of the order of operations for evaluating the expression, and then define functions h, g and f in that order.

First you evaluate e^3x + 1.

h(x) = e^(3x) + 1.

Second, evaluate the square root:

g(x) = sqrt(x)

so that g( h(x) ) = sqrt( h(x) ).

Third, add 2:

f(x) = x + 2

so that f( g( h(x) ) ) = g( h(x) ) + 2.