Question

Find the inverse function f of the function f. Find the range of f and the domain and range of f f(x)=-tan (x + 3)-2-3-2…2-3 Find the inverse, f ,off. f (x) (Use integers or fractions for any numbers in the expression.) The range of f(x) is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) The domain of f (x) is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) The range of f i (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Answer 1

f(x) = -tan (x + 3) - 2, -3 -pi/2 < x > -3 + pi/2 i.e f = D rightarrow R is defined by f(x) = -tan (x + 3) - 2, where D = (-3 - pi/2, -3 + pi/2) y = -tan (x + 3) - 2 rightarrow -tan (x + 3) = y + 2 rightarrow tan (x + 3) = -y - 2 rightarrow x + 3 = tan^-1 (-y - 2) rightarrow x = -3 - tan^-1(y + 2) therefor f^-1: R rightarrow D is defined by f^-1 (x) = -3 - tna^-1 (x + 2) see that lim f(x) = infinity x rightarrow - 3 - pi/2 lim_x rightarrow -3 + pi/2 f(x) = -infinity therefor range of f(x) is (-infinity, infinity). Domain of f^-1 = R. = (-infinity, infinity) the range of f^-1 = (-3 - pi/2, -3 + pi/2)