Author: Yinson Tso

Let f(x) and g(x) be function whose domains are real numbers. Then the domain of (f/g)x is also a real number.

False – if the denominator were to be 0, the equation will turn to be undefined.

Let g(x) be a function and assume x=2 is in the domain of g(x). Then g(2) is a real number.

True – g(2) is the output and 2 is a real number within the domain.

The inverse of a one-to-one function is always a one-to-one function

True – As it says, one-to-one is the same

Let f(x) and g(x) be polynomial functions. Then (f∘g)(x) must also be a polynomial function

True – Polynomials multiplied by polynomials will make a more complex polynomial, (x^{2}-6)(x^{2}+2x) = x^{4}+2x^{3}-6x{2}-12x

A vertical line cannot represent the graph of a function

True – It’s not a graph anymore, it’s just a vertical line at that point. x=0

10

a) f(2) = -1

b) f(1) = 2 (because of solid dot)

c) f(5) = undefined (not on graph)

d) Determine the domain of f(x). (Not fully sure how accurate this is)

(-inf,-2)U(-2,1]U(1,4]

e) Is there an x-value such that f(x) = 1? If so, find all such x-values.

x=-2 and x=1

Please let me know if you find any errors, would help me and any one else that were confused.