Inverses (VCE SSCE Mathematical Methods): Flashcards

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Inverses
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Relationship between exponential and logarithmic functions

They are inverses of each other

Value of loga(ax)\log_a(a^x)

xx

Value of alogaxa^{\log_a x}

xx (for x>0x > 0)

Method to find inverse of a function

Swap xx and yy, then solve for yy

Domain of f1f^{-1} in terms of ff

Range of ff

Range of f1f^{-1} in terms of ff

Domain of ff

Line of reflection for inverse functions

y=xy = x

Technique to solve for a variable in an exponent

Take logarithms of both sides

Inverse of f(x)=axf(x) = a^x (where a>0a > 0, a1a \neq 1)

g(x)=logaxg(x) = \log_a x

Reason loga(ax)=x\log_a(a^x) = x and alogax=xa^{\log_a x} = x hold

Functions are inverses - they reverse each other's operations

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