A-LevelMathematicsFunctions9709/12 · May/June 2011 · Q65 Marks
The function f is defined by f : x → (x+3)/(2x-1), x ∈ R, x ≠ 1/2.
- (i)Show that ff(x) = x.[3]
- (ii)Hence, or otherwise, obtain an expression for f⁻¹(x).[2]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- [3] (i) ff(x) = ( (x+3)/(2x-1) + 3 ) / ( 2(x+3)/(2x-1) - 1 ); B1 Replacing "x" twice - must be correct; M1 Correct algebra – clearing (2x - 1); A1 AG - all correct.; = ( (x+3 + 3(2x-1))/(2x-1) ) / ( (2(x+3) - (2x-1))/(2x-1) ) = (x+3+6x-3)/(2x+6-2x+1) = (7x)/7 = x
- [2] (ii) y = (x+3)/(2x-1); M1 Attempt to make x the subject and complete method; A1 co; f⁻¹(x) = (x+3)/(2x-1); or since ff(x) = x, f⁻¹(x) = f(x) = (x+3)/(2x-1) (M1, A1)
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