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alyssamiller401
01.08.2019 •
Mathematics
Verify that f has an inverse. then use the function f and the given real number a to find (f −1)'(a). (hint: see example 1. if an answer does not exist, enter dne.) function real number f(x) = x + 2 x − 6 , x > 6 a = 3
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Ответ:
f(x) = x + 2 x − 6 > f(x) = 3x− 6
The function is continuous in the interval (-∞,∞)
y=3x-6 >3x=y+6> x=(y+6)/3
Interchange x and y to find the inverse function
(f −1)(x)=(x+6)/3> (x/3)+2
Apply derivative with respect to x
(f −1)'(x)=1/3
for all values of x (f −1)'(x)=1/3
therefore
for a=3 (f −1)'(a)=1/3
Ответ: