Practise questions · Salam Academy

SA-9709-P1-FN2-0012 marksL1 FoundationCalculatorEvaluate fg(a)

f(x)=2x+3

and

g(x)=x^2-1

. Find

gf(2)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0042 marksL1 FoundationCalculatorExpressions

f(x)=2x+3

. Find an expression for

ff(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-G012 marksL1 FoundationCalculatorEvaluate fg(a)

f(x)=2x+3

and

g(x)=x^2-1

. Find

fg(2)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-Q011 markL1 FoundationCalculatorEvaluate fg(a)

To work out

fg(x)

you apply

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SA-9709-P1-FN2-Q021 markL1 FoundationCalculatorExistence & range

The composite

fg

exists when

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SA-9709-P1-FN2-Q031 markL1 FoundationCalculatorExpressions

For a function

f

, the notation

f^2(x)

means

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SA-9709-P1-FN2-0022 marksL2 StandardCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Find an expression for

fg(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0032 marksL2 StandardCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Find an expression for

gf(x)

, simplified.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0053 marksL2 StandardCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Solve

fg(x)=19

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0071 markL2 StandardCalculatorExistence & range

f(x)=\sqrt{x-1}

for

x\ge1

, and

g(x)=3-x^2

for

x\in\mathbb{R}

. Which statement is true?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0092 marksL2 StandardCalculatorExpressions

f(x)=x^2+2

for

x\in\mathbb{R}

, and

g(x)=\dfrac{1}{x-1}

for

x\ne1

. Find an expression for

gf(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0143 marksL2 StandardCalculatorExistence & range

f(x)=x+4

and

g(x)=\sqrt x

. (i) Find

gf(5)

. (ii)

gf(x)

is defined for

x\ge k

. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0063 marksL3 ExamCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Solve

gf(x)=0

.

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SA-9709-P1-FN2-0082 marksL3 ExamCalculatorExistence & range

f(x)=\sqrt{x-1}

for

x\ge1

, and

g(x)=x+k

for

x\ge0

. Find the least value of

k

for which

fg

exists.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0102 marksL3 ExamCalculatorExistence & range

With

gf(x)=\dfrac{1}{x^2+1}

for

x\in\mathbb{R}

, find the greatest value of

gf(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0123 marksL3 ExamCalculatorExpressions

f(x)=x-5

and

g(x)=x^2

. Find the value of

x

for which

fg(x)=gf(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0114 marksL4 ChallengingCalculatorExpressions

f(x)=ax+b

, where

a>0

. Given that

ff(x)=9x-8

, find

a

and

b

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0135 marksL5 ExtensionCalculatorExistence & range

f(x)=3x-1

for

0\le x\le1

, and

g(x)=x^2+2x

for

x\in\mathbb{R}

. The range of

gf

is

p\le gf(x)\le q

. Find

p

and

q

.

Salam Academy Original Practice · Proposed mark scheme

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