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1.2.22 Inverse and composite functions (A-level only)

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Question 31

The function fff is defined by

f(x)=13(x2+2),x≥0 f(x) = \frac{1}{3}(x^2 + 2), \quad x \geq 0 f(x)=31​(x2+2),x≥0
a.

Find the range of fff.

[1]
bi.

Find f−1(x)f^{-1}(x)f−1(x).

[2]
bii.

State the range of f−1(x)f^{-1}(x)f−1(x).

[1]
c.

State the transformation which maps the graph of y=f(x)y = f(x)y=f(x) onto the graph of y=f−1(x)y = f^{-1}(x)y=f−1(x).

[1]
d.

Find the coordinates of the point of intersection of the graphs of y=f(x)y = f(x)y=f(x) and y=f−1(x)y = f^{-1}(x)y=f−1(x).

[3]

1.2.22 Inverse and composite functions (A-level only) Questions

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