O-LevelAdditional MathematicsFunctions4037/11 · May/June 2017 · Q48 Marks
State the range of f.
- (a)(i)State the range of f.[1]
- (a)(ii)Find f⁻¹ and state its domain.[4]
- (b)It is given that g(x) = x² + 5 and h(x) = lnx for x > 0. Solve hg(x) = 2.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] f>5, f(x)>5
- [B1] y-5 = e-4x or x-5 = e-4y
- [B1] -4x = ln (y-5)/3 or -4y=ln(x-5)/3
- [B1] leading to f⁻¹(x) = -1/4 ln ((x-5)/3) or f⁻¹(x) = 1/4 (ln3 - ln(x-5)) or f⁻¹(x) = -1/4 (ln(x-5) - ln3)
- [B1] Domain x > 5
- [B1] ln(x² + 5) = 2
- [B1] x² +5 = e²
- [B1] x=1.55 or better or √e² -5
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →