Please help with 32 and 33, thank you.
1 answer:
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
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Answer:
Area covered by the fences will be 16.1 unit²
Step-by-step explanation:
Let the first parabola is represented by the function f(x) = 6x²
and second parabola by g(x) = x² + 9
point of intersection of the graphs will be determined when f(x) = g(x)
6x² = x² + 9
5x² = 9
x² = 1.8
x = ± 1.34
Now we will find the area between these curves drawn on the graph.
Area =
=
=
=
=
= 16.1 unit²