State whether the following mappings are one-to-one, many-to-one, one-to-many or many-to-many.
(i)
(ii)
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State whether the following mappings are one-to-one, many-to-one, one-to-many or many-to-many.
(i)
(ii)
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The function f(x) is defined as
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.
Write down the range of f(x) .
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The function f(x) is defined as
Work out the range of f(x) .
If the domain of f(x) is changed to what is the range of f(x)?
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The functions f(x) and g(x) are defined as follows
Write down the range of f(x) .
Find
(i)
Solve the equation f(x) = g(x).
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The graph of y = f(x) is shown below.
(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.
On the diagram above sketch the graph of y = f −1(x).
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On the same axes, sketch the graphs of y = f(x) and where
Label the points at which the graphs intersect the coordinate axes.
Solve the equation .
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The function f(x) is defined as
Show that f(x) can be written in the form
Explain why the inverse of f(x) does not exist and suggest an adaption to its domain so the inverse does exist.
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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Solve the equation .
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The functions f(x) and g(x) are defined as follows
Find
Write down f−1(x) and state its domain and range.
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The functions f(x), g(x) are defined as follows
Sketch the graph of y = fg(x) , stating the coordinates of all points where the graph intercepts the coordinate axes.
How many solutions are there to the equation fg(x) = 5 ?
How many solutions are there to the equation fg(x) = 9 ?
Write down the solutions to the equation fg(x) = 0.
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