O-LevelAdditional MathematicsLogarithmic and exponential functions4037/11 · May/June 2021 · Q57 Marks
The functions f and g are defined as follows. f(x) = x² + 4x for x ∈ R g(x) = 1+e²x for x∈R
- (a)Find the range of f.[2]
- (b)Write down the range of g.[1]
- (c)Find the exact solution of the equation fg(x) = 21, giving your answer as a single logarithm.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [2] M1for a valid method to find the least value of x² + 4x
- [2] A1 for f > -4, y ≥ –4 or f(x) ≥ 4
- [1] B1 Allow y>1or g(x)>1
- [4] M1
- [4] M1 Dep for quadratic in terms of e2x and attempt to solve to obtain e²* = k
- [4] M1 Dep on both previous M marks, for attempt to solve e2x = / k
- [4] A1
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