Dominic has $420 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include taxes. He bu
1 answer:
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Answer:
32. ∛((x-7)/4) = f^(-1)(x)
33. -10x - 9
Step-by-step explanation:
32. We want to switch f(x) and x, and then solve for f(x) to get the inverse.
x = 4f(x)³ + 7
subtract 7 from both sides
x -7 = 4f(x)³
divide both sides by 4
(x-7)/4 = f(x)³
cube root both sides
∛((x-7)/4) = f(x)
make f(x) f^(-1)(x) because this is now the inverse
∛((x-7)/4) = f^(-1)(x)
the second answer is correct
33. for composition, we can treat (f · g) (x) as attached picture (content filter!), so we plug g(x) into f(x). This results in
2(-5x-7) + 5
expand
-10x - 14 + 5
add
-10x - 9
the second answer is correct
Answer:
See below
Step-by-step explanation:
We start by dividing the interval [0,4] into n sub-intervals of length 4/n
Since f is increasing in the interval [0,4], the upper sum is obtained by evaluating f at the right end of each sub-interval multiplied by 4/n.
Geometrically, these are the areas of the rectangles whose height is f evaluated at the right end of the interval and base 4/n (see picture)
but
so the upper sum equals
When both
and
tend to zero and the upper sum tends to
