# Function of a Function

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We are solving "function of a function" type problems
So here's one [reads problem]
we'll start with first one - finding f of g of x
f(x)=x^2+1
that means that f of whatever happens to be in here
is that thing squared plus one
so
f of g of x is g of x squared plus one
now
g(x) was 2x+1 so we replace g(x) with 2x+1
so f(2x+1) = (2x+1) squared plus 1
Finished! We can break brackets and tidy up, but you've done the hard bit.
Next question is to find g of f of x so
g(x) is 2x + 1 so
g of whatever is in there is 2 times whatever plus one
So just like before g of f of x is 2 times f of x plus 1
so g of x squared plus one ...
because that's what f of x was - x squared plus 1 ...
g of x squared plus one is 2 times( x squared plus one) plus one
again you can break brackets and tidy up but that's the hard work finished.
Thank you for watching!