Label each statement TRUE or FALSE.

Question

a. The sum of two one-to-one functions is one-to-one.
b. The product of two one-to-one functions is one-to-one.
c. If f is a one-to-one function and k is a real number (constant), then the function g(x)=k*f(x)is one-to-one.

Answer 1

a) - yes
the sum of ax+b and cx+d is still linear

b) - no
the product of ax+b with cx+d produces a term in x^2. Quadratics are not one-to-one

c) - yes
multiplying a linear like ax+b by a constants keeps it linear.

Answer 2

yes