Question

If f(x)=x^2-x and g(x)=x+1, determine f (g(x)) in simplest from

Answer 1

f(g(x)) is basically replacing the x with g(x).

So, f(x)=(g(x))^2 - g(x)

g(x), in turn, equals x+1

Replace g(x) with x+1

(x+1)^2 - (x+1)

Expand: x^2+x+x+1 - x - 1

Cancel out x and 1

f(g(x))=x^2+x

If you require factoring it's

f(g(x))=x(x+1)

Answer 2

f(g(x)) = x^2 +x

Explanation:

To find f(g)(x) , we substitute g(x) in for x in the function f(x)

f(x) = x^2 -x

f(g(x)) = g(x)^2 -g(x)

= (x+1)^2 - (x+1)

= (x+1)*(x+1) - (x+1)

FOIL the square

(x+1) (x+1)

First x*x = x^2

outer x*1 = x

inner 1*x = x

last 1*1 =1

Add them together

x^2 + x+x+1 = x^2+2x+1

f(g(x)) = (x+1)*(x+1) - (x+1)

= x^2+2x+1 -(x+1)

Distribute the -1

= x^2 +2x+1 -x-1

= x^2 +x