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Which statement about the functions f(x)=2x+5 and g(x)=6x+15 is true? Responses g(x)=f(x+3) g open argument x close argument equals f open argument x plus 3 close argument g(x)=f(3x) g open argument x close argument equals f open argument 3 x close argument g(x)=f(x)+3 g open argument x close argument equals f open argument x close argument plus 3 g(x)=3⋅f(x)

Respuesta :

Let's evaluate each statement:

1. g(x) = f(x + 3)

  - Substituting the expressions for f(x) and g(x), we get:

    6x + 15 = 2(x + 3) + 5

    6x + 15 = 2x + 6 + 5

    6x + 15 = 2x + 11 (Incorrect)

2. g(x) = f(3x)

  - Substituting the expressions for f(x) and g(x), we get:

    6x + 15 = 2(3x) + 5

    6x + 15 = 6x + 5 (Incorrect)

3. g(x) = f(x) + 3

  - Substituting the expressions for f(x) and g(x), we get:

    6x + 15 = 2x + 5 + 3

    6x + 15 = 2x + 8 (Incorrect)

4. g(x) = 3 . f(x)

  - Substituting the expressions for f(x) and g(x), we get:

    6x + 15 = 3(2x + 5)

    6x + 15 = 6x + 15 ) (Correct)

So, the correct statement is g(x) = 3 . f(x).