In algebra, how are these solved? I have been struggling with these

Given that f(x)=x^2+2 and g(x)=2x-5, find each of the following.
(FoG)(1) and (GoF)(-3)

(FoG)(1) = f(g(1)) = (2(1)-5)^2 + 2 = 11

(GoF)(-3) = g(f(-3)) = 2((-3)^2 + 2) - 5 = 17

f(x) = x^2 + 2

g(x) = 2x - 5

f o g)(x) = f(g(x))
to find (f o g)(1) or f(g(1)), evaluate g(1), then substitute that value into f(x)...

g(1) = - 3
f(- 3) = 11
(f o g)(1) = - 11

you try to do (g o f)(- 3)

read your textbook...practice.

[(g o f)(- 3) = g(f(- 3)) = 17]

I'm not exactly sure about your notation,

but:
f(g(1)) = (2(1)-5)^2 + 2 = 11
g(f(-3)) = 2((-3)^2+2)-5 = 6

g(1) = - 3; f(-3) = 9 + 2 = 11

(f o g)(1) = f(g(1)) by definition of f o g; so (fog)(1) = 11

Same idea:

f(-3) = 11; g(11) = 22 - 5 = 17

(gof))(-3) = g(f(-3)) = g(11) = 17

(FoG)(1)=11 , (GoF)(-3)=17