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

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

Step-by-step 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

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)