# Answer to Question #21101 in Trigonometry for Kristen Woods

Question #21101

if f(x)=x^2+3 and g(x)=3x-1

then find the following

1g. (f * g)(x)

1h. (f * g)(1)

1i. (g * f)(x)

then find the following

1g. (f * g)(x)

1h. (f * g)(1)

1i. (g * f)(x)

Expert's answer

1g. (f * g)(x)

(f*g)(x) = f (g(x)) = (3x-1)^2 + 3 = 9x^2 - 6x + 4

1h. (f * g)(1)

(f *g)(1) = 9*1^2 - 6*1 + 4 = 1

1i. (g * f)(x)

(g * f)(x) = g(f(x)) =3*(x^2+3) -1 = 3x^2 + 8

(f*g)(x) = f (g(x)) = (3x-1)^2 + 3 = 9x^2 - 6x + 4

1h. (f * g)(1)

(f *g)(1) = 9*1^2 - 6*1 + 4 = 1

1i. (g * f)(x)

(g * f)(x) = g(f(x)) =3*(x^2+3) -1 = 3x^2 + 8

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