maths help plz..?

Question

your told f(x)= 2x/3-5 g(x)=x/2+3

now am told to find for these ones:
(a) fg(x)
(b) gf(10)
(c) gf(x)

Answer 1

PROBLEM A:
f( g(x) )

Wherever you have x in f(x), insert g(x).

f(x) = 2x/3 - 5
f(g(x)) = 2(g(x))/3 - 5
f(g(x)) = 2(x/2 + 3)/3 - 5

Distribute the 2:
f(g(x)) = (x + 6)/3 - 5

Distribute the 3:
f(g(x)) = x/3 + 2 - 5

Combine the numbers:
f(g(x)) = x/3 - 3

PROBLEM B:
g(f(10))

f(10) = 2(10)/3 - 5
f(10) = 20/3 - 5
f(10) = 20/3 - 15/3
f(10) = 5/3

g(f(10)) = g(5/3)
= (5/3)/2 + 3
= 5/6 + 3
= 5/6 + 18/6
= 23/6
= 3 5/6

PROBLEM C:
g(f(x)) = (2x/3 - 5)/2 + 3
= 2x/6 - 5/2 + 3
= x/3 - 5/2 + 3
= x/3 - 5/2 + 6/2
= x/3 - 1/2

Answer 2

Your told? Do you mean "You're told?"

Now am told? Do you mean " We are asked to find?"

These ones? Do you mean "Find these expressions?"

Use language precisely if you want someone to understand what you are trying to say. And it will clear up your own confusion.

Also, was the problem, (a) for example, written as you have shown or as

f o g (x) ?