Performing Compositions of Functions
Compute compositions of functions in Grade 10 algebra by evaluating f(g(x)): substitute the inner function into the outer function and simplify the resulting expression.
Key Concepts
New Concept The composite function $f(g(x))$ uses output values from $g(x)$ as input values for $f(x)$. The composition is written $f(g(x))$ or $(f \circ g)(x)$.
What’s next Next, you’ll practice building and evaluating these composite functions and see why the order of operations is so critical.
Common Questions
How do you evaluate f(g(x)) for f(x)=x²+1 and g(x)=3x?
Substitute g(x) into f: f(g(x)) = f(3x) = (3x)²+1 = 9x²+1.
Is function composition commutative — does f(g(x)) always equal g(f(x))?
No. Function composition is generally not commutative. For f(x)=x+1 and g(x)=2x: f(g(x))=2x+1 but g(f(x))=2(x+1)=2x+2, which are different.
How do you find the domain of a composite function f(g(x))?
The domain is all x-values in the domain of g for which g(x) is also in the domain of f. Check both restrictions simultaneously.