Inverses (VCE SSCE Mathematical Methods): Quizzes

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Inverses
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Which type of function is the inverse of an exponential function?

Logarithmic function

What is the value of loga(ax)\log_a(a^x) for all xRx \in \mathbb{R}?

xx

What is the value of alogaxa^{\log_a x} for all positive xx?

xx

What is the first step to find the inverse of a function?

Swap xx and yy, then solve for yy

If the domain of ff is R\mathbb{R}, what is the range of f1f^{-1}?

R\mathbb{R}

What is the inverse of f(x)=ex+2f(x) = e^x + 2?

f1(x)=loge(x2)f^{-1}(x) = \log_e(x - 2)

What is the domain of f1(x)=loge(x2)f^{-1}(x) = \log_e(x - 2)?

(2,)(2, \infty)

What is the inverse of f(x)=2loge(x1)+3f(x) = 2\log_e(x - 1) + 3?

f1(x)=ex32+1f^{-1}(x) = e^{\frac{x-3}{2}} + 1

Solving P=AektP = Ae^{kt} for tt gives which expression?

t=1kloge(PA)t = \frac{1}{k}\log_e\left(\frac{P}{A}\right)

Reflection in which line swaps coordinates to find an inverse?

y=xy = x

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