We are given that g (x) = 2f (-x) + 3. To produce the base function f (x) we can first shift down 3 units as,

g₁(x) = g (x) - 3 = 2 f (-x) + 3 -3 = 2 f (-x).

We can now vertically shrink g₁(x) by a factor of 1/2 as,

g₂(x) = 1/2g₁(x) = 1/2(2f (-x)) = f (-x).

To recover f (x) we can now reflect g₂(x) across the y-axis as,

g₃(x) = g₂(-x) = f (- (-x)) = f (x).

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