VICMath MethodsQuick questions

Unit 2

Quick questions on Inverse and composite functions: VCE Math Methods Unit 2 Year 11

9short 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 linear?

Show answer

f(x) = 3x + 2

. Swap:

x = 3y + 2

. Solve:

y = (x - 2)/3

What is quadratic with restriction?

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f: [0, \infty) \to [0, \infty)

f(x) = x^2

. Swap:

x = y^2

. Solve (positive root, since range of

f^{-1}

[0, \infty)

y = \sqrt{x}

What is exponential?

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f(x) = 2^x

. The inverse is

f^{-1}(x) = \log_2(x)

(0, \infty)

What is wrong root sign on quadratic inverse?

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Solving

y = x^2

gives

x = \pm\sqrt{y}

; the correct sign depends on the restricted domain.

What is composite order confusion?

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(f \circ g)(x) = f(g(x))

: apply

g

first. Many students apply

f

first by mistake.

What is domain ignored in composite?

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f(g(x))

requires

x

in the domain of

g

AND

g(x)

in the domain of

f

What is q1?

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For

f(x) = x + 4

and

g(x) = 3x

, find

(f \circ g)(x)

and

(g \circ f)(x)

. [2+2 marks]

What is q2?

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Find the inverse of

f(x) = 5x - 1

and verify

f(f^{-1}(2)) = 2

. [3 marks]

What is q3?

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State why

f(x) = x^2

\mathbb{R}

has no inverse, and give a domain restriction that fixes this. [2 marks]