Question

Find the indicated values where g(t)=t^2-t and f(x)=1+x g(f(0))+f(g(0))

Answer 1

g(f(0))+f(g(0)) = 1

Explanation:

We need to find g(f(0))+f(g(0)).

g(t)=t²-t and f(x)=1+x.

f(0) = 1 + 0 = 1

g(f(0)) = g(1) = 1²-1 = 0

g(0) = 0²-0 = 0

f(g(0)) = f(0) = 1+0 = 1

So

g(f(0))+f(g(0)) = 0 + 1 = 1

Answer 2

1

Explanation:

First find f(0) and g(0). These are the values where x=0 in each function.

f(0) = 1+0 = 1

g(0) = 1^2 - 1 = 1-1 = 0

So f(0) = 1 and g(0) = 0.

Now substitute f(0) = 1 into g(t).

g(1) = 1^2 -1 = 1-1 = 0.

So g(f(0)) = 0.

Now substitute g(0) = 0 into f(t).

f(0) = 1 + 0 = 1.

So f(g(0)) = 1.

Add the values 0 and 1 to get 0+1 = 1.