Function Notation and Identities (VCE SSCE Mathematical Methods): Quizzes

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Function notation and identities
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What does adding logarithms correspond to for their arguments?

Multiplying arguments

If f(x)=log⁡exf(x) = \log_e x, what does f(x)−f(y)f(x) - f(y) equal?

f(xy)f(\frac{x}{y})

If f(x)=exf(x) = e^x, what does f(x+y)f(x + y) equal?

f(x)f(y)f(x)f(y)

What does adding exponents correspond to for exponential values?

Multiplying exponential values

For which function does f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y) hold for all xx and yy?

f(x)=2xf(x) = 2x

Why doesn't f(x)=x+2f(x) = x + 2 satisfy f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y)?

The constant term prevents it

For f(x)=1xf(x) = \frac{1}{x}, what identity holds for all non-zero real xx and yy?

f(x)+f(y)=(x+y)f(xy)f(x) + f(y) = (x + y)f(xy)

Why must xx and yy be non-zero for f(x)=1xf(x) = \frac{1}{x}?

f(x)=1xf(x) = \frac{1}{x} is undefined at x=0x=0

For f(x)=cos⁡xf(x) = \cos x with x=0,y=πx = 0, y = \pi, what does f(0+π)f(0 + \pi) equal?

−1-1

How many counterexamples are needed to show a property doesn't hold for all values?

One counterexample

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