Three functions are listed below. Which of these functions have an inverse funct
ID: 2883038 • Letter: T
Question
Three functions are listed below. Which of these functions have an inverse function on the domain (-infinity, infinity)? f(x) = x^2 g(x) = 3x + 1 h(x) = sin(x) A colony of bacteria grows at a rate proportional to its size. Initially, there are 100 cells in the colony. The colony triples in size every 2 hours. How many cells are present after 7 hours? Suppose f^-1 is the inverse function of a differentiable function off and f(3) = 4, f'(3) = 7/4, then (f^-1)'(4) = If f(x) = ln|x^2 - 1|, then f'(x) =Explanation / Answer
(a) f(x) = x^2 has an inverse on the domain (-, )
Let f^-1(x) = y then f(y) = x
y^2 = x
y = ± x
f^-1(x) = ± x
(b) g(x) = 3x + 1 has an inverse on the domain (-, )
Let g^-1(x) = y then f(y) = x
3y + 1 = x
y = (x - 1)/3
g^-1(x) = (x - 1)/3
(c) h(x) = sin x does not have an inverse on the domain (-, ).