Math  /  Algebra

Question1 The functions ff and gg are defined by f(x)=2ln(x+3),x>3f(x)=2 \ln (x+3), x>-3 and g(x)=ekx3,xRg(x)=\mathrm{e}^{k x}-3, x \in \mathbb{R}, where kk is a constant. The function g is the inverse of function f . (a) Determine the value of kk. [4 marks] (b) Sketch the graphs of ff and gg on the same axes. [5 marks]

Studdy Solution
Verify that the graphs of f f and g g are reflections over the line y=x y = x .
- Check that for any point (a,b)(a, b) on f f , the point (b,a)(b, a) is on g g .
The value of k k is:
12 \boxed{\frac{1}{2}}

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