Question

If f(x) and f₁(x) are inverse of each other and f(x)=2x+5, what is f₁(8)?

a. -1
b. 3/2
c.41/8
d.23

Answer 1

To find f₁(8), use the fact that f(x) and f₁(x) are inverse functions. Swap x and f(x) in the equation for f(x), solve for x to find the inverse function f₁(x), then substitute 8 for x to find f₁(8). The answer is 3/2.

Step-by-step explanation:

To find f₁(8), we need to use the fact that f(x) and f₁(x) are inverse functions. Since f(x) = 2x + 5, we can find the inverse function f₁(x) by switching the roles of x and f(x) and solving for x. So, let's start by expressing f(x) as y and swapping x and y in the equation:

y = 2x + 5

Now, solve for x:

x = (y - 5) / 2

The inverse function f₁(x) is found by replacing y with x:

f₁(x) = (x - 5) / 2

To find f₁(8), plug in 8 for x:

f₁(8) = (8 - 5) / 2 = 3/2

Therefore, the answer is b. 3/2.