To rewrite the equation [tex]\( 25x^4 - 625y - 500 = 0 \)[/tex] as a function of [tex]\( x \)[/tex], we need to isolate [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]. Here is the step-by-step process:
1. Start with the given equation:
[tex]\[ 25x^4 - 625y - 500 = 0 \][/tex]
2. Isolate the term involving [tex]\( y \)[/tex] by adding [tex]\( 625y \)[/tex] to both sides:
[tex]\[ 25x^4 - 500 = 625y \][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing both sides by 625:
[tex]\[ y = \frac{25x^4 - 500}{625} \][/tex]
4. Simplify the expression inside the fraction:
[tex]\[ y = \frac{25x^4}{625} - \frac{500}{625} \][/tex]
5. Simplify each term:
[tex]\[ y = \frac{25}{625}x^4 - \frac{500}{625} \][/tex]
6. Reducing the fractions:
[tex]\[ y = \frac{1}{25}x^4 - \frac{4}{5} \][/tex]
Thus, the function [tex]\( f(x) \)[/tex] that represents [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[ f(x) = \frac{1}{25}x^4 - \frac{4}{5} \][/tex]
The correct answer is:
A. [tex]\( f(x) = \frac{1}{25} x^4 - \frac{4}{5} \)[/tex]
