To find the inverse of the function [tex]\( f(x) = 5x + 3 \)[/tex], we need to follow these steps:
1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
y = 5x + 3
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[
x = 5y + 3
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
x = 5y + 3
\][/tex]
Subtract 3 from both sides:
[tex]\[
x - 3 = 5y
\][/tex]
Divide by 5:
[tex]\[
y = \frac{x - 3}{5}
\][/tex]
Thus, the inverse function is:
[tex]\[
f^{-1}(x) = \frac{x - 3}{5}
\][/tex]
Now, compare this result with the given options:
A. [tex]\( f^{-1}(x) = 3 - 5x \)[/tex]
B. [tex]\( f^{-1}(x) = \frac{x - 3}{5} \)[/tex]
C. [tex]\( f^{-1}(x) = 5 x - 3 \)[/tex]
D. [tex]\( f^{-1}(x) = \frac{x - 5}{3} \)[/tex]
The correct option is [tex]\( \boxed{B} \)[/tex].
