The function \( f \) is given by \( f(x)=9.25^{x} \). Which of the following is an equivalent form for \( f(x) \) ? (A) \( f(x)=9.5^{\left(x \frac{1}{2}\right)} \) (B) \( f(x)=3.5^{(2 x)} \) (C) \( f(x)=9.5^{(x)}(2) \) (D) \( f(x)=9.5^{(2 x)} \)

To find an equivalent form for the function \( f(x) = 9.25^{x} \), we need to simplify the expression and compare it with the given options. Given function: \( f(x) = 9.25^{x} \) Let's simplify the expression by expressing 9.25 as a power of 9.5: \( 9.25 = 9.5 \times 0.95 \) Now, we can rewrite the function as: \( f(x) = (9.5 \times 0.95)^{x} \) Using the properties of exponents, we can simplify this expression further: \( f(x) = 9.5^{x} \times 0.95^{x} \) Comparing this with the given options: (A) \( f(x) = 9.5^{\left(x \frac{1}{2}\right)} \) (B) \( f(x) = 3.5^{(2x)} \) (C) \( f(x) = 9.5^{(x)}(2) \) (D) \( f(x) = 9.5^{(2x)} \) The equivalent form for \( f(x) \) is \( f(x) = 9.5^{x} \times 0.95^{x} \), which matches option (D) \( f(x) = 9.5^{(2x)} \).