select the correct answer.\nwhich function defines $(f \\div g)(x)$?\n$f(x) = (3.6)^{x+2}$\n$g(x) =…

select the correct answer.\nwhich function defines $(f \\div g)(x)$?\n$f(x) = (3.6)^{x+2}$\n$g(x) = (3.6)^{3x+1}$\n\\bigcirc a. $(f \\div g)(x) = (3.6)^{4x+3}$\n\\bigcirc b. $(f \\div g)(x) = (1.8)^{-2x+3}$\n\\bigcirc c. $(f \\div g)(x) = (1.8)^{3x^2+7x+2}$\n\\bigcirc d. $(f \\div g)(x) = (3.6)^{-2x+1}$

select the correct answer.\nwhich function defines $(f \\div g)(x)$?\n$f(x) = (3.6)^{x+2}$\n$g(x) = (3.6)^{3x+1}$\n\\bigcirc a. $(f \\div g)(x) = (3.6)^{4x+3}$\n\\bigcirc b. $(f \\div g)(x) = (1.8)^{-2x+3}$\n\\bigcirc c. $(f \\div g)(x) = (1.8)^{3x^2+7x+2}$\n\\bigcirc d. $(f \\div g)(x) = (3.6)^{-2x+1}$

Answer

Explanation:

Step1: Recall the exponent rule for division

When dividing two exponential functions with the same base, we use the rule ( \frac{a^m}{a^n} = a^{m - n} ). Here, the base ( a = 3.6 ), ( m = x + 2 ) (from ( f(x) )), and ( n = 3x + 1 ) (from ( g(x) )).

Step2: Apply the exponent rule

Calculate ( (f \div g)(x)=\frac{f(x)}{g(x)}=\frac{(3.6)^{x + 2}}{(3.6)^{3x+1}} ). Using the rule ( a^m\div a^n=a^{m - n} ), we subtract the exponents: ( (x + 2)-(3x + 1) ). Simplify the exponent: ( x + 2-3x - 1=-2x + 1 ). So, ( (f \div g)(x)=(3.6)^{-2x + 1} ).

Answer:

D. ((f \div g)(x) = (3.6)^{-2x+1})