Question

Precalc help needed, find g ° f!

Answer 1

g o f = -[f(x)]² + 3 = -(|x|)² + 3 = -x² + 3 = g(x)

Explanation:

g o f = g [ f(x) ]

This means replace the x of g(x) with f(x):

g o f = -[f(x)]² + 3 = -(|x|)² + 3

As x² ≥ 0 for any value of x (whether it be positive or negative), then -(|x|)² + 3 = -x² + 3 = g(x)

So g o f = g(x)