Practise questions · Salam Academy

SA-9709-P1-FN3-0062 marksL1 FoundationCalculatorFind the inverse

f(x)=5-2x

,

x\in\mathbb{R}

. Find

f^{-1}(1)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0071 markL1 FoundationCalculatorOne-one

Which of these functions, each with domain

\mathbb{R}

, is one-one?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-G012 marksL1 FoundationCalculatorFind the inverse

f(x)=3x-5

,

x\in\mathbb{R}

. Find

f^{-1}(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-Q011 markL1 FoundationCalculatorDomain of the inverse

The domain of

f^{-1}

is always

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-Q021 markL1 FoundationCalculatorFind the inverse

f^{-1}(x)

means

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-Q031 markL1 FoundationCalculatorOne-one

A function is one-one if

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0013 marksL2 StandardCalculatorFind the inverse

f(x)=\dfrac{4}{x-2}

for

x>2

. Find

f^{-1}(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0031 markL2 StandardCalculatorDomain of the inverse

f(x)=(x-2)^2+1

for

x\ge2

. The domain of

f^{-1}

is

x\ge c

. State

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0042 marksL2 StandardCalculatorOne-one

f(x)=x^2-4x+7

for

x\ge k

. Find the least value of

k

for which

f

is one-one.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0093 marksL2 StandardCalculatorDomain of the inverse

f(x)=\sqrt{x+3}

for

x\ge-3

. (i) Find

f^{-1}(6)

. (ii) The domain of

f^{-1}

is

x\ge c

. State

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0121 markL2 StandardCalculatorOne-one

Why does

f(x)=x^2-2x

,

x\in\mathbb{R}

, have no inverse?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0023 marksL3 ExamCalculatorQuadratic inverses

f(x)=(x-2)^2+1

for

x\ge2

. Find

f^{-1}(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0083 marksL3 ExamCalculatorFind the inverse

f(x)=3x-4

. Solve the equation

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

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0103 marksL3 ExamCalculatorFind the inverse

f(x)=2x-1

and

g(x)=x^3

. Find

(fg)^{-1}(15)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0113 marksL3 ExamCalculatorQuadratic inverses

f(x)=8-(x-3)^2

for

x\ge3

. Find

f^{-1}(4)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0054 marksL4 ChallengingCalculatorQuadratic inverses

f(x)=x^2+6x+4

for

x\le-3

. Find

f^{-1}(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0136 marksL5 ExtensionCalculatorQuadratic inverses

f(x)=x^2-4x+1

for

x\le1

. (i) The range of

f

is

f(x)\ge r

. Find

r

. (ii) Find

f^{-1}(x)

. (iii) Find

f^{-1}(6)

.

Salam Academy Original Practice · Proposed mark scheme

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