The Function Machine
Compose functions by passing the output of one into the other.
Let and .
Input
{{ s1.inputVal }}
{{ s1.inputVal }}
Machine g
{{ s1.gOut }}
{{ s1.gOut }}
Machine f
{{ s1.fOut }}
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Drag input to Machine g
Drag output to Machine f
Composition complete!
Build the Expression
Find by substituting into the of .
Drop g(x) here
Grab this
Simplifies to:
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Drag expression to substitute
Substituted correctly!
Build the Inverse
The inverse function undoes everything does, in reverse order. Let .
Forward f(x)
x
y
Inverse f⁻¹(x)
x
y
extension
Drag operations to build inverse
Inverse built!
Graph the Inverse
The graph of is a reflection of across the line .
Drag the pink points to reflect them across the dashed line. Swap their (x,y) coordinates!
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Drag points to reflect
Perfect reflection!
🏆
Master of Functions!
You've successfully composed functions and unlocked their inverses both algebraically and graphically.