find the domain of the composite function of fog
f(x)=x^2+8;g(x)�ãx-5
f(g) = g^2+8 = √(x-5)^2+8 = x-5+8 = x+3
To find the domain of the composite function fog, we need to find the values of x for which the composition of f and g is defined.
The composition of f and g, denoted as fog, is defined as f(g(x)). In other words, we substitute the expression for g(x) into f(x).
So, substituting g(x) = x - 5 into f(x) = x^2 + 8, we have:
fog(x) = f(g(x)) = f(x - 5) = (x - 5)^2 + 8
Now, to find the domain of fog, we need to consider any restrictions on x that would make the expression (x - 5)^2 + 8 undefined.
The expression (x - 5)^2 is always defined because squaring a number is always possible. However, adding 8 to the square of (x - 5) does not impose any additional restrictions on the domain.
Therefore, the domain of fog is all real numbers, or in interval notation, (-∞, ∞).
Therefore, the domain of the composite function fog is (-∞, ∞).