The diagram shows the graph of radians.
Explain why is a function.
Write down the range of .
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The diagram shows the graph of radians.
Explain why is a function.
Write down the range of .
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.
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It is given that .
Write down the range of .
Find and state its domain.
On the axes below, sketch the graph of and the graph of . Label each curve and state the intercepts on the coordinate axes.
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[1]
[3]
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.
The graph of intersects the line at two distinct points. On the axes below, sketch the graph of and hence sketch the graph of .
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It is given that , where and are non-zero constants.
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Find the range of .
Explain why has an inverse.
Find .
State the domain of .
Given that , find the exact solution of .
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Solve .
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The functions and are defined as follows.
Find the range of .
Write down the range of .
Find the exact solution of the equation , giving your answer as a single logarithm
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Given that the minimum value of occurs when , explain why has an inverse.
On the axes below, sketch the graph of and the graph of . Label each graph and state the intercepts on the coordinate axes.
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for
for
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The function is defined by.
Sketch the graph of and hence sketch the graph of on the axes below.
The function is defined by .
[4]
[2]
[1]
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Find the range of and of .
Find the exact solution of .
Find the solution of .
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