O-LevelAdditional MathematicsFunctions4037/11 · May/June 2019 · Q89 Marks
It is given that f(x) = 5e^x -1 for x ∈ R. It is given also that g(x) = x²+4 for x ∈ R.
- (i)Write down the range of f.[1]
- (ii)Find f⁻¹ and state its domain.[3]
- (iii)Find the value of fg(1).[2]
- (iv)Find the exact solutions of g²(x) = 40.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] f > -1 or f(x) > -1, y > -1, (−1,∞), {y:y>−1}
- [M1] a complete valid method to obtain the inverse function
- [A1] y = ln((x+1)/5) or f⁻¹(x) = ln((x+1)/5) oe
- [B1] FT their (i) or correct Domain x > -1 or (-1,∞)
- [M1] evaluation using correct order of operations
- [A1] awrt 741 or 5e^5-1
- [M1] correct use of g²
- [M1] DepM1 for forming and solving a quadratic in x²
- [A1] x = ±√2 only
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 →