Question

If f(x) = x² + 5 and g(x) = 3x, find (f . g)(x) and (g . f)(x) .

Answer 1

see explanation

Explanation:

to evaluate (f ￮ g)(x) , substitute x = g(x) into f(x)

(f ￮ g)(x)

= f(g(x))

= f(3x)

= (3x)² + 5

= 9x² + 5

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to evaluate (g ￮ f)(x) substitute x = f(x) into g(x)

(g ￮ f)(x)

= g(x² + 5)

= 3(x² + 5)

= 3x² + 15