Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths WJEC
  5. Question bank

3.2.3 Algebra and Functions (A-level only)

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859
Question 39

The functions fff and ggg are defined by

f(x)=12−3xfor x≤4 f(x) = \sqrt{12 - 3x} \quad \text{for } x \le 4 f(x)=12−3x​for x≤4 g(x)=1xfor x≠0 g(x) = \frac{1}{x} \quad \text{for } x \ne 0 g(x)=x1​for x=0

The function hhh has the maximum possible domain and is defined by h(x)=gf(x)h(x) = gf(x)h(x)=gf(x).

a.

Find an expression for h(x)h(x)h(x).

[1]
b.

Find the domain of hhh.

[2]
c.

Show that h−1(x)=4−13x2h^{-1}(x) = 4 - \frac{1}{3x^2}h−1(x)=4−3x21​.

[3]

3.2.3 Algebra and Functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2.3 Algebra and Functions (A-level only)