Question: The function f is such that f(x) = 2x + 1 for x . The function g is such that g(x) = 8

The function f is such that f(x) = 2x + 1 for x ∈ ℝ.

The function g is such that g(x) = 8 − ax − bx2 for x ≥ k, where a, b and k are constants.

The function fg is such that fg(x) = 17 − 24x − 4x2 for x ≥ k.

a. Find the value of a and the value of b.

b. Find the least possible value of k for which g has an inverse.

c. For the value of k found in part b, find g−1(x).

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