H(x)=(x+1)^2 find functions f(x) and g(x) so that h(x)=f(g)(x))

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Step-by-step explanation:

There are numerous possible solutions. Perhaps the simplest is to look at what happens to x in the expression for h(x).

This suggests that f(x) will square the result of g(x), and that g(x) will add 1 to x:

  g(x) = x +1

  f(x) = x²

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Check

  h(x) = f(g(x)) = f(x+1) = (x+1)² . . . . as required

Additional comment

For some (almost) arbitrary function g(x), the function f(x) can include its inverse (to get the value of x+1), then perform the square. If g(x) involves powers of x, then f(x) only needs to do enough of an inverse to find (x+1)². Here's a relatively simple example.

  g(x) = 2x+3

  f(x) = (x -1)²/4

Then h(x) = f(g(x)) = f(2x +3) = ((2x +3) -1)²/4 = (2(x+1))²/4 = (x+1)²

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step-by-step explanation: