Let F,g,h,p: R>R be defined by f(x)=x-1, g(x)=x+2, h(x)=sinx and p(x)=2x^4+4x^3-6x^2. Find the inverse of f(x)÷g(x) at x=0? (B) Find the domain and range of the function x-3÷x+2

Question

Let F,g,h,p: R>R be defined by f(x)=x-1, g(x)=x+2, h(x)=sinx and p(x)=2x^4+4x^3-6x^2. Find the inverse of f(x)÷g(x) at x=0? (B) Find the domain and range of the function x-3÷x+2

Answer 1

Part 1

f(x) = (x-1)/(x+2)

y = (x-1)/(x+2)

x = (y-1)/(y+2)

x(y+2) = y-1

xy+2x = y-1

2x+1 = y-xy

2x+1 = y(x-1)

(2x+1)/(x-1) = y

f^-1(x) = (2x+1)/(x-1)

f^-1(0) = (2(0)+1)/(0-1) = 1/-1 = -1

Part 2

f(x) = (x-3)/(x+2) has a vertical asymptote at x=-2 and a horizontal asymptote at y=1 (as the numerator and denominator's degrees are the same as well as their respective coefficients). Thus, the function's domain is (-∞,-2)∪(-2,∞) and the range is (-∞,1)∪(1,∞).

Hope this helped!