Find [f o g](-3) and [g o f](-3) if f(x)=x^2 - 4x+5 and g(x)= x-2?

Answer 1

f ( g (- 3) ) = f ( - 5 ) = 25 + 12 + 5 = 42
g ( f (-3) ) = g (9 + 12 + 5) = g ( 26 ) = 24

Answer 2

Given:
f(x) = x^2 - 4x + 5
g(x) = x - 2

[f o g(-3)] = (-3 - 2)^2 - 4(-3) + 5

All you are doing is plugging in -3 for x into the g(x) equation, and then plugging THAT into the f(x) equation.

= (-5)^2 + 12 + 5
= 25 + 17
= 42

Same for the next one. Except the g and the f are switched.

[g o f(-3)] = [(-3)^2 - 4(-3) + 5)] - 2

= 9 + 12 + 5 - 2
= 21 + 3
= 24