Functions, graphs and inverses practice question 1
Let and . Evaluate the composition below.
In , which function gets the 3 first, and which one acts on its output?
means . Work from the inside out.
Start by computing , then feed that single number into .
A whole number.
Theory UBC Math 100 §1.5CLP-1 §0.5Key resultsAssumed from precalculus
Worked solution
Strategy
Composition is evaluated inside first. Find the output of the inner function at 3, then use that output as the input to the outer function.
Working
Unpack the notation. The right-hand function acts first.
Evaluate the inner function at the given input.
Substitute that single value into the outer function.
Answer
The answer is 15.
Check
As one formula, f(g(x)) = 2(x² + 1) − 5 = 2x² − 3, which at x = 3 is 18 − 3 = 15.
Where this goes wrong
Composing in the wrong order and computing g(f(3)) = g(1) = 2. The function written on the left of the circle is applied last, not first.
The idea behind it
The functions, graphs and inverses lesson, a figure to move, in a few steps
Saved in this browser only.