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Functions and Graphs

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Question 216

The function fff is defined by

f(x)=3x+5x−4,x≠4 f(x) = \frac{3x + 5}{x - 4}, \quad x \neq 4 f(x)=x−43x+5​,x=4
a.

Find f−1(x)f^{-1}(x)f−1(x).

[3]
b.

Show that

ff(x)=ax+bcx+d ff(x) = \frac{ax + b}{cx + d} ff(x)=cx+dax+b​

where a,b,ca, b, ca,b,c and ddd are integers to be found.

[3]
c.

The point P(5,20)P(5, 20)P(5,20) lies on the curve with equation y=f(x)y = f(x)y=f(x).

Find the point to which PPP is mapped when y=f(x)y = f(x)y=f(x) is transformed to the curve with equation y=3f(2x)−10y = 3f(2x) - 10y=3f(2x)−10.

[3]
Markscheme

Functions and Graphs Questions

  1. A Level
  2. /Maths
  3. /Functions and Graphs

471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.

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