Practise questions · Salam Academy

SA-9709-P1-FN4-0061 markL1 FoundationCalculatorIntersections

For an increasing function

f

, the graphs of

y=f(x)

and

y=f^{-1}(x)

can only meet

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0072 marksL1 FoundationCalculatorReflect in y = x

The point

(-1,4)

is reflected in the line

y=x

. State the coordinates of its image.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-G012 marksL1 FoundationCalculatorReflect in y = x

The point

(2,7)

lies on the graph of

y=f(x)

. State the coordinates of the corresponding point on the graph of

y=f^{-1}(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-Q011 markL1 FoundationCalculatorReflect in y = x

The graph of

y=f^{-1}(x)

is the reflection of

y=f(x)

in

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-Q021 markL1 FoundationCalculatorReflect in y = x

y=f(x)

has a horizontal asymptote

y=5

. The graph of

y=f^{-1}(x)

has

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-Q031 markL1 FoundationCalculatorReflect in y = x

When sketching

y=f(x)

and

y=f^{-1}(x)

on the same axes, you should

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0012 marksL2 StandardCalculatorIntersections

f(x)=2x+3

. Find the

x

-coordinate of the point where the graphs of

y=f(x)

and

y=f^{-1}(x)

meet.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0042 marksL2 StandardCalculatorReflect in y = x

f(x)=\sqrt{x+2}

for

x\ge-2

. The graph of

y=f^{-1}(x)

crosses the

y

-axis at

(0,c)

. Find

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0051 markL2 StandardCalculatorReflect in y = x

f(x)=\dfrac{1}{x-2}+3

for

x>2

. The graph of

y=f^{-1}(x)

has a vertical asymptote

x=k

. State

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0081 markL2 StandardCalculatorSelf-inverse

f(x)=3-x

,

x\in\mathbb{R}

. What can you say about

f^{-1}

?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0101 markL2 StandardCalculatorReflect in y = x

f(x)=x^2+3

for

x\ge1

. The domain of

f^{-1}

is

x\ge c

. State

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0122 marksL2 StandardCalculatorIntersections

f(x)=4x-9

. Find the coordinates of the point where

y=f(x)

meets

y=f^{-1}(x)

, giving the

x

-coordinate.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0021 markL3 ExamCalculatorIntersections

f(x)=x^2+2

for

x\ge0

. Which statement about the graphs of

y=f(x)

and

y=f^{-1}(x)

is true?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0033 marksL3 ExamCalculatorIntersections

f(x)=x^2-6

for

x\ge0

. Find the

x

-coordinate of the point where the graphs of

y=f(x)

and

y=f^{-1}(x)

meet.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0093 marksL3 ExamCalculatorSelf-inverse

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

for

x\ne2

. Show that

f

is self-inverse, and hence find

f^{-1}(6)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0112 marksL3 ExamCalculatorReflect in y = x

f(x)=x^3+8

,

x\in\mathbb{R}

. State (i) where

y=f^{-1}(x)

crosses the

x

-axis (ii) where it crosses the

y

-axis.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0134 marksL5 ExtensionCalculatorIntersections

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

for

x\ge2

. Find the

x

-coordinates of all points where the graphs of

y=f(x)

and

y=f^{-1}(x)

meet.

Salam Academy Original Practice · Proposed mark scheme

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