Problema Solution

let f(x)=(1/5)x+(-7), where -3 is less than or equal to x, and where x is less than or equal to 0. The domain of f^-1 is the interval [A,B] when A=? and B=?

Answer provided by our tutors

Domain of f^ -1 is the range of f.


Let y = (1/5)x - 7, where -3 </= x </= 0


-3 <= x <= 0


Multiplying throughout by ( 1/5),


(-3/5) <= x/5 <= 0


Subtracting 7 throughout


(-3/5) - 7 <= (x/5) - 7 <= 0 - 7


-38/5 <= y <= -7.


Hence,


range of f = domain of f^ -1 = [ -38/5, -7 ].


Hence, A = -38/5 and B = -7


The domain of f^-1 is the interval [A,B] when A=-38/5 and B=-7