If f(x)=x and g(x)=x+1 find the function and its domain:
1. gof
2. fof
(gof)(x) means you substitute the whole expression of f(x) to g(x):
(gof)(x) = g(f(x)) = f(x) + 1
(gof)(x) = x + 1
for #2, we do the same,, we substitute f(x) to f(x):
(fof)(x) = f(x)
(fof)(x) = x
hope this helps~ :)
Sweet! Thanks
To find the function gof, we need to evaluate g(f(x)).
Since f(x) = x, we replace every instance of x in g(x) with f(x) to get g(f(x)) = g(x+1).
Therefore, the function gof is g(f(x)) = x + 1.
To determine the domain of gof, we need to consider the restrictions, if any, on the values of x for which the function is defined.
Since f(x) = x, it is defined for all real numbers.
Similarly, g(x) = x + 1 is defined for all real numbers.
Therefore, the domain of gof, which is g(f(x)) = x + 1, is also all real numbers.
Now let's move on to fof.
To find the function fof, we need to evaluate f(f(x)).
Since f(x) = x, we replace every instance of x in f(x) with f(x) to get f(f(x)) = f(x).
Therefore, the function fof is f(f(x)) = f(x) = x.
To determine the domain of fof, we again need to consider any restrictions on the values of x.
Since f(x) = x, it is defined for all real numbers.
Therefore, the domain of fof, which is f(f(x)) = x, is also all real numbers.