Question

f(x)= the absolute value of x^2-6x-7
a) Find a piecewise defined function that has no absolute value involved
b) Let g(x)=f(x) for x is greater than or equal to 7 find an expression of
g^-1(x)
c. give the domain and range of g^-1(x)

Answer 1

Since |x| = x when x >= 0
|x|= -x when x < 0

we need to find where f(x) >= 0 and f(x) < 0

f(x) = (x-7)(x+1)

f >= 0 where x <= -1 or x >= 7

This should get you going.