FUNCTIONS: In the space provided, type the answer in descending order as it applies without any spaces between the letters, numbers, or symbols.

Type the composition image of the given functions:

f(x) = x2 + 2x − 6 and g(x) x + 5.

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1 Resposta

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Hi Lucy S.,

For (g o f)(x), we are looking for g(x) of f(x), which can also be written as g[f(x)], meaning substitute f(x) for any x in g(x).

So with g(x) = x + 5, replace all x's with f(x): g[f(x)] = f(x) + 5

And for f(x) = x2 + 2x - 6, we can substitute for f(x): g[x2 + 2x - 6] = (x2 + 2x - 6) + 5

To reiterate:

(g o f)(x) = g[f(x)]

(g o f)(x) = f(x) + 5

(g o f)(x) = (x2 + 2x - 6) + 5

(g o f)(x) = x2 + 2x - 1

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