Question

what is the inverse of f(x)=8-x^2

Answer 1

say y=8-x^2 and try writing x in terms of y

Answer 2

construct and simplify the difference
quotient f(h+h)-f(x)/h
The difference quotient is=
f(x)=x^2-8
Now, we can just substitute these into the expression:
(f(x+h)-f(x))/h=(%28%28x%2Bh%29%5E2-8%29-%28x%5E2-8%29%29%2Fh+)/h=%28x%5E2%2B2xh%2Bh%5E2-8-x%5E2%2B8%29%2Fh=%282xh%2Bh%5E2%29%2Fh=2x%2Bh
That is the answer. In calculus, we would take the limit as h goes to zero. If h is 0, 2x+h=2x. This gives the derivative of the function f(x)=x^2+c, c arbitrary. I hope you find that information interesting

Answer 3

momo1999, you're finding the derivative. they only need the inverse. no calculus involved.

Answer 4

f (x) = 2x – 1
y = 2x – 1
y + 1 = 2x
(y + 1)/2 = x
(x + 1)/2 = y
(x + 1)/2 = f –1(x)
like that