Operations on Functions

Sums, differences, products, quotients and composition of functions, and their domains.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

If f(x) = x² − 4 and g(x) = x + 2, what is (f + g)(x)?
If f(x) = 3x + 1 and g(x) = x², what is the value of (f ∘ g)(2)?
For f(x) = 3x + 1 and g(x) = x², which expression is (g ∘ f)(x)?
If f(x) = x² − 9 and g(x) = x − 3, which is (f/g)(x) in simplest form, with its restriction?
If f(x) = √x and g(x) = x − 5, the domain of (f ∘ g)(x) is x ≥ a. What is the value of a?
If f(x) = 1/x and g(x) = x − 4, what is the domain of (f ∘ g)(x)?
The graphs of the line y = f(x) and the parabola y = g(x) are shown. What is the value of f(g(1))?
The graphs of the line y = f(x) and the parabola y = g(x) are shown. What is the value of (g ∘ f)(−1)?
Which pair of functions gives h(x) = √(x² + 1) as h(x) = f(g(x))?
If f(x) = x² − 2x and g(x) = x + 3, what is the value of (f·g)(3)?