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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 243

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

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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