To find the inverse of the function [tex]\( f(x) = 8x + 4 \)[/tex], follow these steps:
1. Express [tex]\( f(x) \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ y = 8x + 4 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = 8y + 4 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
- First, isolate the term with [tex]\( y \)[/tex]:
[tex]\[ x - 4 = 8y \][/tex]
- Then, divide both sides by 8:
[tex]\[ y = \frac{x - 4}{8} \][/tex]
Therefore, the inverse function of [tex]\( f(x) = 8x + 4 \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x - 4}{8} \][/tex]
Among the given options, the correct answer is:
B. [tex]\( f^{-1}(x)=\frac{x-4}{8} \)[/tex]
