let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.
f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1
let's call this new function hh. so we have:
{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1
we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.
method 1: substitute x=2x=2 into the combined function hh.
h(x)
h(2)
=3x+1
=3(2)+1
=7
since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).
first, let's find f(2)f(2):
f(x)
f(2)
=x+1
=2+1
=3
now, let's find g(2)g(2):
g(x)
g(2)
=2x
=2⋅2
=4
so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.
notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!
