using f(x)=4x-5, find
f^-1 o f
I'm sure I could solve this if your question made a bit more since.
What's with f^-1? That doesn't mean anything. Is it F^2-1?
Please clarify and you'll get your answer very fast. :)
it's f to the power of -1, then i think it's called composite f. Like you know when you get the problems fog of gof? it's like that except fof and the first f is raise to -1 power. Thanks
Ah I see!
Sorry for the blind-sightedness. :P
I believe your answer is
f(x)=1/4x-5
No worries, Thank you
first of all,
if f(x) = 4x - 5 , then
f^-1(x) = (x+5)/4
then f^-1 o f = f^-1(f(x))
= f^-1(4x-5)
= ((4x-5) + 5)/4
= x
To find the composite function f^(-1) o f, we need to apply two steps.
Step 1: Find f^(-1) of f(x)
To find f^(-1) of f(x), we need to find the inverse of the function f(x). The inverse function undoes the original function.
Given f(x) = 4x - 5, let's find its inverse.
Step 1.1: Replace f(x) with y
y = 4x - 5
Step 1.2: Swap x and y
x = 4y - 5
Step 1.3: Solve for y
x + 5 = 4y
(x + 5) / 4 = y
So, the inverse function of f(x) is f^(-1)(x) = (x + 5) / 4.
Step 2: Find f^(-1) o f
To find f^(-1) o f, we need to evaluate the composite function by substituting f(x) = 4x - 5 into f^(-1)(x).
Substituting f(x) = 4x - 5 into f^(-1)(x), we get:
f^(-1) o f(x) = f^(-1)(4x - 5) = [(4x - 5) + 5] / 4
Simplifying the expression, we get:
f^(-1) o f(x) = (4x) / 4 = x
Therefore, f^(-1) o f(x) = x.