Question

find the {g(f(x))}and {f(g(x))}. are they equal?
g(x)=x-2
f(x)=x^2+x-12

Answer 1

Hello, you just have to compose the functions. For the first one:\[g(f(x))=[f(x)]-2=[x^2+x-12]-2\]Do you see how f(x) took the place of x in g(x)=x-2?

Answer 2

So you'd keep going to simplify:\[g(f(x))=x^2+x-14\]

Answer 3

For the other one,\[f(g(x))=[g(x)]^2+[g(x)]-12=[x-2]^2+[x-2]-12\]

Answer 4

So\[f(g(x))=x^2-4x+4+x-2-12= x^2+3x-10\]

Answer 5

When you compare the results, they're not the same function.

Answer 6

They're trying to show you that in general,\[f(g(x)) \ne g(f(x))\]

Answer 7

yeah, you're welcome.