VCE Maths Methods - Inverse functions
Inverse functions - one to one
2
• Inverse functions - from graphs
• Inverse functions - rules
• Inverse functions - from equations
• Finding inverse functions - one to one.
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Inverse Functions in VCE Maths Methods, Lecture notes of Calculus
Every one to one function has an inverse function, f-1(x). ... The graph of an inverse function can be found from mirroring the graph around the line y = x.
Typology: Lecture notes
2021/2022
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Inverse functions - one to one
- Inverse functions - from graphs
- Inverse functions - rules
- Inverse functions - from equations
- Finding inverse functions - one to one.
Inverse functions - from graphs
y intercept = 1 Asymptote: y = 0 x intercept = 1 Asymptote: x = 0 y = e x y = log e x
Inverse functions - from equations
y = x 2
x intercept = 6 y intercept = - y intercept = 6 x intercept = - y y = 2 x + 6
x
f (x ) : y = 2 x + 6 f − 1 (x ) : x = 2 y + 6 2 y = x − 6 y = x 2
Finding inverse functions - one to one.
- (^) Let f:(a, ∞ ) → R,where f(x)=x^2 − 6x.
- If a is the smallest real number such that f has an inverse function, fi nd the value of a and the inverse f − 1 (x).
- This is a quadratic function (many to one).
- Either side of the turning point, the function will be one to one.