Question

If f(x)= x-5 and g(x)= -3x + 2, find f(g(«)

Answer 1

Let:

$f(x)=x^2-5$

and

$g(x)=-3x+2$

then the compositive f(g(x)) would be:

$f(g(x))=f(-3x+2)=(-3x+2)^2-5$

this is equivalent to:

$f(g(x))=f(-3x+2)=((-3x)^2-2(6x)+4)^{}-5$

this is equivalent to

$f(g(x))=f(-3x+2)=9x^2-12x+4^{}-5\text{ = }9x^2-12x\text{ -1}$

then the correct answer is the last one, that is:

$f(g(x))\text{= }9x^2-12x\text{ -1}$