Question

Если f(x)= 2^x+1 , то f^-1(7) =

Answer 1

F(7)=2^7+1=129
Отсюда 1/f(7)=1/129.

Answer 2

To find the inverse of a function, you need to swap the roles of x and y and solve for y. Let's solve for f^-1(x):

Given: f(x) = 2^x + 1

Step 1: Swap x and y x = 2^y + 1

Step 2: Solve for y Subtract 1 from both sides: x - 1 = 2^y

Step 3: Take the logarithm base 2 of both sides to isolate y: log2(x - 1) = y

Now, the inverse function is f^-1(x) = log2(x - 1).

To find f^-1(7), simply substitute x with 7:

f^-1(7) = log2(7 - 1) f^-1(7) = log2(6)

Using a calculator, you can compute the approximate value:

f^-1(7) ≈ 2.58496