First question:
If f(x) = 2x+1 and g(x) = x - 3
find f - g of 4.
First combine the two functions to find what f-g is:
f(x) - g(x) = 2 x + 1 - (x - 3) = 2 x + 1 - x + 3 = x + 4
So now find the value of this expression for x=4:
f - g (4) = (4) + 4 = 8
Second question:
Is the following relation a function?
{ (1, 5) , (2, -3); (3, 5); (4, 7) }
This relationship IS a function because for every element of the Domain (1, 2, 3, and 4) there is only one associated value of y.
Third question:
If j(x) = Square root (x - 6), find j(15)
So we replace x with 15 in the function's expression:
j(15) = Square root (15 - 6) = Square root (9) = 3
Then j(15) = 3
Fourth question:
If m(x) = 3 x + 4 and n(x) = x + 2
evaluate n + m of 6
So we proceed to add the two given expressions:
n(x) + m(x) = x + 2 + 3 x + 4 = 4 x + 6
So now we estimate the value of this new expression for x = 6:
4 (6) + 6 = 24 + 6 = 30
In the case of addition or subtraction of functions, you can also do:
f(x) = 2 x + 1 and g(x) = x - 3
and to calculate f - g at x = 4, you can do:
f(4) = 2 (4) + 1 = 9
g(4) = 4 - 3 = 1
and subtract them: 9 - 1 = 8
Not sure if this is shorter or easier than the other method for you. To me they are kind of equivalent.