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3 years ago

8

Function Composition: Let the function

3+6x" alt="f(x)= 3+6x" align="absmiddle" class="latex-formula"> , determine:

1 answer:

V125BC [204]3 years ago

4 0

Answer:

<u>Given </u>

f(x) = 3 + 6x

A

<u>Find the inverse of f(x):</u>

x = 3 + 6f⁻¹(x)
6f⁻¹(x) = x - 3
f⁻¹(x) = (x - 3) / 6

B

f · f⁻¹( ∛5/6) =
f( f⁻¹( ∛5/6)) =
f((∛5/6 - 3)/6) =
3 + 6((∛5/6 - 3)/6) =
3 + ∛5/6 - 3 =
∛5/6

C

f · f⁻¹(x) =
f(f⁻¹(x)) =
f((x - 3)/6) =
3 + 6(x - 3)/6 =
3 + x - 3 =
x

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If we want the new line to be written in slope-intercept form, we need to find the new value of the y-intercept. The equation of the line is ...

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A rhombus has four 6-inch sides and two 120-degree angles. From one of the vertices of the obtuse angles, the two latitudes are

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We begin with finding the angles a and b that from the drawing attached you can see that a=b.

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Next, in the image you can see that the lines coming from the angle at the top 120 degrees vertex, divide the opposite sides by half, thus making two triangles with one side of 6 in and another of 3 in.

We can say from the drawing as well:

Area(A)+Area(B)+Area(C)=Area(rhomboid)

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So, starting with Area(A)

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Area(B)=Area(rhomboid)-Area(A)-Area(C)

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$h=[tex]6*cos(30)=5.20in$ The 30 degrees come from: 120-30-60=30, since the latitudes split the 120 angle in two equal parts and one that is the half of the obtuse angle.

Area(rhomboid)=5.20*6= $31.2 in^{2}$

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