Question

Given f(x) = (x+4/6), solve for f⁻¹(7).
a) 1
b) 24
c) 32
d) 38

Answer 1

To solve for the inverse function f⁻¹(7), we first find the inverse of f(x) = (x+4)/6, which is f⁻¹(x) = 6x-4. Then we substitute x with 7, giving us f⁻¹(7) = 38.

Step-by-step explanation:

The student is asking to solve for the inverse function, f⁻¹(x), of f(x) = (x+4)/6 when f⁻¹(7) is given. The process to find the inverse consists of replacing f(x) with y, switching x and y and then solving for y:

• Let y = (x+4)/6
• Switch x and y to obtain x = (y+4)/6
• Multiply both sides by 6 to get 6x = y + 4
• Subtract 4 from both sides to find y = 6x - 4
• Now, solve for f⁻¹(7) by setting x to 7: y = 6(7) - 4 which equals 42 - 4

Therefore, f⁻¹(7) = 38, which corresponds to choice d.