Edexcel A Level Maths: Pure

Topic Questions

2.8 Functions (A Level Only)

1
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4 marks

State whether the following mappings are one-to-one, many-to-one, one-to-many or many-to-many.

(i)      straight f colon space x rightwards arrow from bar x squared

(ii)     straight f colon space x rightwards arrow from bar 3 x space plus space 1 space

(iii)    

straight f colon space x rightwards arrow from bar left parenthesis x space plus space 1 right parenthesis cubed

(iv)
straight f colon space x rightwards arrow from bar space plus-or-minus space square root of x

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2a
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3 marks

The function f(x) is defined as

straight f left parenthesis x right parenthesis space equals space x to the power of 2 space end exponent plus space 2 x space minus space 3 space space space space space space space space space space x element of straight real numbers

Sketch the graph of y = f(x) , giving the coordinates of any points where the graph intercepts the coordinate axes and the coordinates of the turning point.

2b
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1 mark

Write down the range of f(x) .

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3a
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2 marks

The function f(x) is defined as

straight f left parenthesis x right parenthesis space equals space x squared space minus space 4 space space space space space space space space space space x greater or equal than 0                         

Work out the range of  f(x) .

 

3b
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1 mark

If the domain of f(x) is changed to x less or equal than 0 comma what is the range of f(x)?

 

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4a
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1 mark

The functions f(x) and g(x) are defined as follows

straight f left parenthesis x right parenthesis space equals space x squared space space space space space space space space space space space space space space space space space space space x element of straight real numbers

straight g left parenthesis x right parenthesis space equals space 4 x space minus space 3 space space space space space space space space space space x element of straight real numbers           

Write down the range of f(x) .

 

4b
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4 marks

Find

(i)      left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis

(ii)
left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis
4c
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2 marks

Solve the equation f(x) = g(x).

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5a
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3 marks

The graph of y = f(x) is shown below.

 2-8-m-q5-edexcel-al-maths-pure

(i)       Use the graph to write down the domain and range of f(x).
(ii)      Given that the point (1, 1) lies on the dotted line, write down the equation of the line.

5b
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2 marks

On the diagram above sketch the graph of y = f −1(x).

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6a
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3 marks

On the same axes, sketch the graphs of  y = f(x) and y space equals space vertical line g left parenthesis x right parenthesis vertical line  where

straight f left parenthesis x right parenthesis space equals space left parenthesis x space plus space 2 right parenthesis squared space space space space space space space space space space x element of straight real numbers

 g left parenthesis x right parenthesis space equals space 2 x space plus space 4 space space space space space space space space space space space x element of straight real numbers

Label the points at which the graphs intersect the coordinate axes.

6b
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2 marks

Solve the equation straight f left parenthesis x right parenthesis space equals space vertical line g left parenthesis x right parenthesis vertical line.

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7a
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2 marks

The function f(x) is defined as

straight f colon space x space rightwards arrow from bar space fraction numerator x squared plus 1 over denominator x squared end fraction space space space space space space space space space space x element of straight real numbers comma space x space not equal to space 0

 Show that f(x) can be written in the form

 straight f colon space x space rightwards arrow from bar space 1 space plus space 1 over x squared

                             

7b
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2 marks

Explain why the inverse of f(x) does not exist and suggest an adaption to its domain so the inverse does exist.

7c
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4 marks

The domain of f(x) is changed to x > 0.
Find an expression for f−1(x)  and state its domain and range.

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8
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3 marks

Solve the equation  vertical line 4 x space plus space 2 vertical line space equals space 5.

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9a
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3 marks

The functions f(x) and  g(x)  are defined as follows

straight f left parenthesis x right parenthesis space equals space 1 half space left parenthesis 4 x space minus space 3 right parenthesis space space space space space space space space space space x element of straight real numbers

g left parenthesis x right parenthesis space equals space 0.5 x space plus space 0.75 space space space space space space space space space x element of straight real numbers

Find

(i)
straight f g left parenthesis x right parenthesis
(ii)
g straight f left parenthesis x right parenthesis
9b
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3 marks

Write down f−1(x) and state its domain and range.

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10a
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4 marks

The functions f(x), g(x) are defined as follows

straight f left parenthesis x right parenthesis space equals space vertical line x minus 9 vertical line space space space space space space space space space space x element of straight real numbers

g left parenthesis x right parenthesis space equals space x squared space space space space space space space space space space space space space x element of straight real numbers                                        

Sketch the graph of y = fg(x) , stating the coordinates of all points where the graph intercepts the coordinate axes.

 

10b
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2 marks

How many solutions are there to the equation fg(x) = 5 ?
How many solutions are there to the equation fg(x) = 9 ?

10c
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2 marks

Write down the solutions to the equation fg(x) = 0.

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