Question 1007540: Given the function f(x)= sqrt (7-5x)
a. find the inverse f^-1(x)
b. Determine (F o f^-1)(x)
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Given f(x)= sqrt(7-5x), we first plug y in for f(x), then switch x for y, and then solve for y...when we get that, we exchange f^-1(x) for y...like this...
y = sqrt(7-5x)
x = sqrt(7-5y)
x^2 = 7 - 5y
5y = 7 - x^2
y = (1/5)(7 - x^2)
f^-1(x) = (1/5)(7 - x^2)
To answer b, remember that a function applied on its inverse or vice-versa has to yield x. Thus
(f o f^-1)(x) = x
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