Monotonicity of Composite Functions (Same Increase/Decrease)
Let functions y = f(u) and u = g(x) be composed to form y = f[g(x)]. If f(u) and g(x) have the same monotonicity (both increasing or both decreasing) on the co…
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CSCA Mathematics Formula Reference
Formula and explanation
Let functions y = f(u) and u = g(x) be composed to form y = f[g(x)]. If f(u) and g(x) have the same monotonicity (both increasing or both decreasing) on the corresponding intervals, then the composite function f[g(x)] is monotonically increasing on that interval. If f(u) and g(x) have opposite monotonicity (one increasing, one decreasing) on the corresponding intervals, then the composite function f[g(x)] is monotonically decreasing on that interval. Note: The domain must be considered.
Related tutorial and examples
Comprehensive Application of Function Properties
Comprehensive Application of Function Properties 1. Core Concepts This section integrates all properties. Complex CSCA problems often combine Monotonicity, Parity, Periodicity, and Symmetry. Three Keys to Solving Problems: 1. Transformation: Use Parity/Periodicity to move the pro…
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