So, a function, f(x), can be applied to any valid 'input'
f(x)=x2+2examples
f(19)=192+2=363f(a)=a2+2f(a+1)=(a+1)2+2[br]=a2+2a=3Basically - you sub whatever's into the bracket wherever there's an x. Even if there's a fraction or w/e (more common in compound functions which I will cover now)
so let's say,
f(x)=x2+2 again
g(x)=x+5What would fg(x) be? You can simply work out g(x) and then do f to g(x). Note that the order is right to left.
But if we express fg(x) in one function, it would be:
(x+5)2+2Yup - it's that easy, just put whatever's set as x, into x.
Compound functions can also be repeated but I've never seen it in a question, you could get gg(x).
Inverting functions functions:
Usually expressed as f^-1(x)
All you have to do is:
Take your function, let's use
f(x)=3x+2.
Replace f(x) with y.
y=3x+2Solve for x
x=3y−2Now swap the x and y around, and then swap the y for
f−1(x)Let me know if anything is unclear