inverse functions
What inverse functions means in Mathematics A-Level, as defined for Pearson Edexcel, WJEC.
Definitions of inverse functions
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Reference: WJEC
Only one-to-one functions possess an inverse function f⁻¹(x), whose domain equals the range of f(x) and whose range equals the domain of f(x).
An inverse function f⁻¹(x) exists if and only if f(x) is one-to-one over its domain, with domain the range of f and range the domain of f.
The functions eˣ and ln x are mutual inverse functions, so composing them in either order returns the input variable.
The relationship in which logₐ(aˣ) = x for all real x, and a^(logₐ x) = x for x > 0.
log_a is the inverse function of a^x, so the two graphs are reflections in y = x.
Topics that use inverse functions
- Exponentials and logarithms (Pearson Edexcel A-Level)
- Algebra and Functions (A2 Unit 3: Pure Mathematics B) (WJEC A-Level)
- Exponentials and logarithms (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
- Overarching themes - Mathematical argument, language and proof (WJEC A-Level)
Related terms
- domain restrictions
- laws of logarithms
- reflection in y = x
- solving exponential equations
- algebraic division
- ambient temperature baseline
- cancelling factors
- carrying capacity
Using inverse functions in the exam
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