f(x) = sqrt(x-3)
g(x) = sqrt(x²+3)
f*g(x) (composition)
= f(g(x))
= f(sqrt(x²+3))
= sqrt(sqrt(x²+3)-3)
The domain of g(x) is (-∞,∞)
and the domain of f(x) is [3,∞).
Therefore the domain of f*g(x) is such that
g(x)≥3.
sqrt(x²+3) ≥ 3
x²+3 ≥ 9
x² ≥ 6
x≥√6 or x≤-√6
Therefore the domain of f*g(x) is
(-∞,-√6]∪[√6,∞)
let f(x)=sqrt(x-3), g(x)=sqrt(x^2+3)
Find a formula for f*g and state the domain of the composition
1 answer