Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2D>Q 5

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(a) $f (x) = \frac{x + a}{b x - 1}$ for $x \in ℝ, x \neq \frac{1}{b}$ , where $a & b$ are constants. Prove that this function is self-inverse.

Important Questions on Functions

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2D>Q 5

(b)

g (x) = \frac{a x + b}{c x + d}

for

x \in ℝ, x \neq - \frac{d}{c}

, where

a, b, c

and

d

are constants. Find the condition for this function to be self-inverse.

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(a) $y = 2 x^{2}$ after translation by $(\begin{array}{l} 0 \\ 4 \end{array})$ .

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(b) $y = 5 \sqrt{x}$ after translation by $(\begin{array}{r} 0 \\ - 2 \end{array})$ .

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(c) $y = 7 x^{2} - 2 x$ after translation by $(\begin{array}{l} 0 \\ 1 \end{array})$ .

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(d) $y = x^{2} - 1$ after translation by $(\begin{array}{l} 0 \\ 2 \end{array})$ .

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(e) $y = \frac{2}{x}$ after translation by $(\begin{array}{r} - 5 \\ 0 \end{array})$ .

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AS and A Level

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(f) $y = \frac{x}{x + 1}$ after translation by $(\begin{array}{l} 3 \\ 0 \end{array})$ .

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AS and A Level

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Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 1

Find the equation of each graph after the given transformation.

(g) $y = x^{2} + x$ after translation by $(\begin{matrix} - 1 \\ 0 \end{matrix})$ .