Answer:
To find the inverse function of f(x) = 4x + 12, we follow these steps:Replace f(x) with y: y = 4x + 12.Swap the variables x and y: x = 4y + 12.Solve for y in terms of x: y = (x - 12) / 4.Therefore, the inverse function of f(x) is f^-1(x) = (x - 12) / 4.Now, we can verify that f(f^-1(x)) = x and f^-1(f(x)) = x as follows:f(f^-1(x)) = f((x - 12) / 4) [substitute f^-1(x) into f(x)]
= 4((x - 12) / 4) + 12 [substitute (x - 12) / 4 into 4x + 12]
= x [simplify]Therefore, f(f^-1(x)) = x.f^-1(f(x)) = ((4x + 12) - 12) / 4 [substitute f(x) into f^-1(x)]
= x / 4 [simplify]Therefore, f^-1(f(x)) = x/4.Since f(f^-1(x)) = x and f^-1(f(x)) = x/4, we have verified that the inverse function of f(x) satisfies the conditions of an inverse function.
Explanation: