Question

Find the inverse function f of the function f. Find the range off and the domain and range of f1 f(x) = - tan (x+5)-1; -50<x< -5 Find the inverse, " off. (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'(x)is 1 (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Answer 1

Soleti no f(x) = -tan (x+5) -1 – 0 Let y = f(x), Then o becomes. y = - tan (x+5) - 1 и и in as tan (x+5) = -y-1 a, X+5 = tań' (-4-1) since - < 2+5< Į as x 2-5 - tam' (1+y) – © Put x = f (y), we get f"(y) = - 5 - tan' (1+y).(Answer). x) = - 5 - tañ. (1+x) | Change the variable - (Answer) y into xe. Since x = fcy) : Then, 15-11 F CI - 5 as-5-7<< <1-5, A Range of f'(x) is | (-5-5-5+7) Answer.

o since '(y) = - 3-tan" (1+y) Since tań' (1+y) exists ye C00,00) Then, f (y) exists tyE(-00,00) A domain of is (-2,00) (Answer) f(x) = - tan (2+5) 1. Since - as <tan (x+5) <0,-<x+5<E W, -< - tan(+5) 200,-Ị <(x+5) <E 0, -i- <-1 - tan (x+ 5) <0-1 av, :- 20 <-1-tan (x+5) <0. a co < 6« <co. : Range of f its (-0,0)) (Answer) | TESTI