Question

Consider the function f(x)=2x‾‾√ 4. if f−1(x) is the inverse function of f(x), find f−1(12).

Answer 1

To find the inverse function f−1(x) of f(x)=2x√4 and evaluate f−1(12), you can switch the roles of x and f(x) in the equation, solve for x, and substitute the given value of x.

Step-by-step explanation:

The function f(x) = 2x√4 is defined as the square root of 4 multiplied by 2x. To find the inverse function f−1(x), we need to switch the roles of x and f(x) and solve for x. So, we have:

x = 2f−1(x)√4

To find f−1(12), we substitute x = 12 into the equation:

12 = 2f−1(12)√4

Solving for f−1(12), we divide both sides by 2√4:

f−1(12) = 12 / (2√4)