To solve the equation [tex]\( f^{-1}(x) = 13 \)[/tex] given that [tex]\( f^{-1}(x) = \frac{2x + 1}{5} \)[/tex], we can follow these steps:
1. Set up the equation:
[tex]\[ \frac{2x + 1}{5} = 13 \][/tex]
2. Eliminate the fraction by multiplying both sides by 5:
[tex]\[ 2x + 1 = 13 \times 5 \][/tex]
[tex]\[ 2x + 1 = 65 \][/tex]
3. Isolate the term with [tex]\( x \)[/tex] by subtracting 1 from both sides:
[tex]\[ 2x = 65 - 1 \][/tex]
[tex]\[ 2x = 64 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{64}{2} \][/tex]
[tex]\[ x = 32 \][/tex]
Thus, the solution to the equation [tex]\( f^{-1}(x) = 13 \)[/tex] is:
[tex]\[ x = 32 \][/tex]
