Algebra 8
4 marks · NormalThe function f is defined by f(x) = 4x + 1.
a) Show, by algebraic method, how to find the inverse function f^{-1}(x).
b) Use your result to find f^{-1}(13).
Show, by algebraic method, how to find the inverse function f^{-1}(x).
Use your result to find f^{-1}(13).
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.
Show answer
(a) f^{-1}(x) = (x-1)/4
(b) 3
Common mistakes: Not switching x and y; Arithmetic mistakes in rearranging; Incorrect substitution
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Writes y = 4x + 1, switches x and y (x = 4y + 1 or similar).
M2 (a) · 1 mark · Rearranges to y = (x-1)/4.
A1 (a) · 1 mark · Writes correct inverse function: f^{-1}(x) = (x - 1)/4 or equivalent.
B1 (b) · 1 mark · Substitutes correctly: f^{-1}(13) = (13-1)/4 = 3.
Worked solution
a) Let y = f(x) = 4x + 1
Swap x and y: x = 4y + 1
Rearrange: x - 1 = 4y, so y = (x - 1)/4
So the inverse is f^{-1}(x) = (x - 1)/4
b) f^{-1}(13) = (13 - 1)/4 = 12/4 = 3