Higher Maths Functions Help?

The notation itself suggests what must be done. Instead of sticking a number in the function, you stick a function in the function. I'll do the first one as an example.

f(x) = 3x - 1

g(x) = 2x + 5

f(g(x)) = 3(2x + 5) - 1

= 6x + 15 - 1

= 6x + 14

Think about this

Ill make an example:

f(x) = 2x

g(x) = 10x+4

g(f(x)) means plug in f(x) into g(x) like this

g(x) = 10x+4

g(f(x)) = 10(2x) + 4

g(f(x)) = 20x + 4

or F of G of X which is f(g(x))

plug in g(x) into f(x) this time

f(x) = 2x

f(g(x)) = 2(10x + 4)

f(g(x)) = 20x + 8

Compound formula.

Basically, you're substituting one formula in to another. fg(x) is shorthand for f(x) when the x = g(x). And the important thing to remember is work outwards, so if it's written fg(x), you use g(x), then f(x).

E.g. i) g(x) = 2x+5, so substitute that in to f(x): 3(2x+5) - 1

Which you can simplify to: gf(x) = 6x + 14

Try the second one for yourself.