Linear functions with the exception of fx x can have at mos

Linear functions (with the exception of f(x) = x) can have at most one fixed point. Quadratic functions can have at most two. Find the fixed points of the function g(x) = x^2 - 12. (Enter you answers as a comma-separated list.) Give a quadratic function whose fixed points are x = -4 and x = 5. f(x) =

Solution

(c)

The fixed points of a function FF are simply the solutions of F(x)=x or F(x)-x.

Hence to find the fixed point of the function g(x)=x²-12, we set g(x)=x and solve for x values. Hence

x²-12=x

x²-x-12=0

(x-4)(x+3)=0

Hence x=-3 and x=4 are the fixed points of the function g(x).

Hence x= -3, 4

(d)

Given that the fixed point are x=-4 and x=5. Hence the function is

f(x)-x=(x+4)(x-5)

f(x)-x=x²-x-20

f(x)=x²-20

Hence the function is f(x)=x²-20