advanced functions/precalculus

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1. The function f(x) = (2x + 3)^7 is the composition of two functions, g(x) and h(x). Find at least two different pairs of functions g(x) and h(x) such that f(x) = g(h(x)).

2. Give an example of two functions that satisfy the following conditions:
- one has 2 zeros
- one has no zeros
- the sum of the functions has 1 zero
Show that your functions satisfy the conditions.

  • advanced functions/precalculus -

    g(x) = x^7
    h(x) = 2x+3

    g(x) = (2x+1)^7
    h(x) = x+1


    f(x) = x^2-1
    g(x) = x^2+1
    (f+g)(x) = 2x^2 (one unique zero, repeated)

    f(x) = 3x+x^2
    g(x) = 2-x^2
    (f+g)(x) = 3x+2 (only a single zero)

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