VICMath MethodsQuick questions

Unit 4

Quick questions on Hybrid functions and inverse functions: VCE Math Methods Unit 4

11short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is continuity at a join?

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A hybrid function is continuous at the join point

x = a

if the left-hand value and right-hand value of

f

agree at

a

What is differentiability at a join?

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A hybrid function is differentiable at the join point

x = a

if it is continuous at

a

AND the left and right derivatives agree:

What are two-constant problems?

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Many Paper 1 hybrid questions give a hybrid function with two unknown constants in one piece, and ask to find the constants such that the function is continuous and differentiable at a specified join.

What is finding

f^{-1}

algebraically?

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To find the inverse of

y = f(x)

What is wrong root sign?

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When solving

y = x^2

for

x

, the answer is

x = \pm \sqrt{y}

. The correct sign depends on the domain restriction.

What is domain and range not swapped?

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The inverse's domain is the original's range, and vice versa. Stating only the original domain misses the swap.

What is continuity matched but differentiability ignored?

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"Continuous and differentiable" requires both conditions. If only continuity is checked, the function may have a kink.

What is differentiability checked without first checking continuity?

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A function that is not continuous at a join cannot be differentiable there. Check continuity first.

What is q1?

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A hybrid function has

f(x) = 3x

for

x \le 2

and

f(x) = x + c

for

x > 2

. Find

c

f

is continuous at

x = 2

. [2 marks]

What is q2?

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For the same join, is

f

differentiable at

x = 2

when

c = 4

? Justify. [2 marks]

What is q3?

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Find the inverse of

f(x) = (x + 2)^2

x \ge -2

. [3 marks]

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