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1.2.22 Inverse and composite functions (A-level only)

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Question 30

The function fff is defined by

f(x)=4x−1x−3,x>3 f(x) = \frac{4x - 1}{x - 3}, \quad x > 3 f(x)=x−34x−1​,x>3
a.

Show, by using calculus, that fff is a decreasing function.

[3]
b.

Find f−1(x)f^{-1}(x)f−1(x).

[3]
c.

(i) Show that ff(x)=ax+bx+cff(x) = \frac{ax + b}{x + c}ff(x)=x+cax+b​ where a,b,a, b,a,b, and ccc are constants to be found. (ii) Deduce the range of ffffff.

[5]

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

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