Let f(x)=-3+5. Find f sub -1 (x)

Question

How do you find find:

f(x)=-3x+5. Find f sub -1(x)

Answer 1

I am guessing that by f sub -1 you mean the inverse of f, which is normally written here as f^-1() and in your text book as f^-1(x).

f(x) =-3x+5  the inverse has to do the opposite of the function so we need to subtract 5 from x and then divide by 3 .  So

f^-1(x)= -1/3(x -5)

 

The check please:

If this is correct then f(f^-1(x)) should equal x for all x in the domain of f.

So, for instance f(6)=-3(6)+5 = -18+5 = -13 and f^-1(-13)= -1/3(-13-5) = -1/3(-18) = 18/3 = 6

Answer 2

f(x) = 3x + 5

 

I think you mean "Find f^-1(x)"?  If not, please re-post the question.  f^-1 is the inverse function of f(x).  Finding it is a 4 step process:

 

Step 1: Replace the f(x) with a y:

 

y = 3x + 5

 

Step 2: Switch the x's and y's:

 

x = 3y + 5

 

Step 3: Solve for y

 

3y + 5 = x

3y = x - 5

y = (1/3)x - 5/3 = f^-1(x)

 

Step 4: Check.  f(f^-1(x)) = x:

 

f(x) = 3x + 5

f(f-1(x)) = 3*f^-1(x) + 5

     = 3((1/3)x - 5/3) + 5

     = x - 5 + 5

     = x

Check!