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The function f is defined by f(x)=e2x−8ex−20. The function is graphed over part of its domain below.
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f(x) has a y-intercept at a, an x-intercept at b, and a horizontal asymptote at y=c.
Write down the value of
a
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c
Find the value of b
Give an expression for f(x) in the form (ex−k)2+h, where k,h∈R.
The graph of y=f(x) has a minimum at P.
Using your answer to part (c), show that P has coordinates (2ln2,−36)
The function g is defined by g(x)=2⋅∣f(x−a)∣−38, where a∈R.
The graph of y=g(x) has a local maximum at the point (ln(4e2),b).
Find the values of
a
b.
The diagram below shows a sketch of y=g(x).
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Find the possible values of k such that g(x)1=k has exactly 3 solutions.
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