Algebra 8
3 marks · NormalGiven the function k(x) = 3x − 4, explain step by step how to find its inverse, and then write down k^{-1}(x).
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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k^{-1}(x) = (x + 4)/3
Also accept: (x + 4)/3
Common mistakes: Not swapping x and y; Mistakes in rearranging equation
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Writes y = 3x − 4 and swaps x and y.
M2 · 1 mark · Rearranges: x = 3y − 4, then x + 4 = 3y, so y = (x + 4)/3.
A1 · 1 mark · Writes k^{-1}(x) = (x + 4)/3.
Worked solution
Let y = 3x − 4
Swap x and y: x = 3y − 4
x + 4 = 3y
y = (x + 4)/3
So the inverse is k^{-1}(x) = (x + 4)/3