Question

Define f(x)=3x−8. If f −1 is the inverse of f, find the value(s) of x for which f(x)=f −1(x).

a) 2
b) 4
c) 6
d) 8

Answer 1

To find the value(s) of x for which f(x) = f inverse (x), set the two equations equal to each other, find the inverse function of f(x), and solve for x.

Step-by-step explanation:

To find the value(s) of x for which f(x) = f-1(x), we can set the two equations equal to each other:

3x - 8 = f-1(x)

We can find the value(s) of x by solving this equation. First, let's find the inverse function of f(x):

Let y = f(x)

Switch x and y:

x = 3y - 8

Solve for y:

3y = x + 8

y = (x + 8)/3

So, the inverse function of f(x) is f-1(x) = (x + 8)/3

Now, set f(x) and f-1(x) equal to each other and solve for x:

3x - 8 = (x + 8)/3

9x - 24 = x + 8

8x = 32

x = 4

Therefore, the value of x for which f(x) = f-1(x) is x = 4. Answer choice b) 4 is correct.