Consider the function f. 1∕x+2

Question

(A) State the domain of f in interval notation.

(B) Find the inverse function of f.

(C) State the domain of the inverse function in interval notation.

(D) State the range of both the function f and its inverse function in interval notation.

Answer 1

domain of y=1/x+2 is all reals except-2 where we have a vertical asymptote (-inf,-2) (-2,inf)

for the inverse function exchange x for y and solve for y so x=1/y+2

y+2 =1/x

y= (1/x) + 2 domains all reals except zero

the range of both functions is all reals (-infinity,+infinity)