Question

find the domain and range of the function:
f(g(x))
With the equations:
f(x)=(x^2)-6
g(x)=2x-3

Answer 1

(2x-3)^2-6 domain is 3/2 and the range is -6

Answer 2

f(g(x))= (2x-3)^2 - 6
4x^2 +9-12x-6
4x^2 -12x +3

So, domain is all the values of x such that \[x \in R \]

RANGE: first find the point with slope=0
so differentiating wrt x
8x-12=0
x=3/2
putting the value of x
f(g(x))=4(3/2)^2 - 12(3/2) + 3
=-6

so, the range is [-6 , infinity]