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Zinaida [17]
3 years ago
7

Suppose a function f has an inverse. If f(2)=6 and f(3)=7, find: f^-1 (f(3))

Mathematics
1 answer:
klemol [59]3 years ago
3 0

9514 1404 393

Answer:

  3

Step-by-step explanation:

The definition of an inverse function is ...

  f^-1(f(x)) = x

Then ...

  f^-1(f(3)) = 3

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Please someone help me..!!!!​
Nikolay [14]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Triple Angle Identity: sin 3A = 3sinA - 4sin³A

\text{Given:}\quad \sin\bigg(\dfrac{\theta}{3}\bigg)=\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)

<u>Proof LHS → RHS</u>

LHS:                                 sin Ф

Let A = Ф/3                     sin 3A

Triple Angle Identity:     3sinA - 4sin³A

Substitute Ф/3 = A:         3sin(Ф/3) - 4sin³(Ф/3)

Substitute sin(Ф/3):         3\bigg(\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)\bigg)-4\bigg(\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)\bigg)^3

\text{Simplify:}\qquad \qquad \dfrac{3m}{2}+\dfrac{3}{2m}-4\bigg(\dfrac{1}{8}\bigg(m^3+3m+\dfrac{3}{m}+\dfrac{1}{m^3}\bigg)\bigg)\\\\.\qquad \qquad \qquad =\dfrac{3m}{2}+\dfrac{3}{2m}-\dfrac{m^3}{2}-\dfrac{3m}{2}-\dfrac{3}{2m}-\dfrac{1}{2m^3}\\\\.\qquad \qquad \qquad =-\dfrac{m^3}{2}-\dfrac{1}{2m^3}\\\\\text{Factor:}\qquad \qquad -\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)

\text{LHS = RHS:}\quad -\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)=-\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)\quad \checkmark\\

7 0
3 years ago
A 5000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest for
Vitek1552 [10]

Answer:

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Step-by-step explanation:

aefaef bajn faefaefaefaefeafaef

5 0
3 years ago
If A=78º, b=16, c=7, what is the area of this triangle?
Andrei [34K]

Answer:

= 54.78 square units

Step-by-step explanation:

We can calculate the area of the triangle using the formula;

Area = 1/2abSinθ ; where a and b is the sides making the angle θ.

Therefore;

Area = 1/2 bc sin C

        = 1/2 × 16 × 7 × Sin 78

        = 8 × 7 × sin 78

        <u>= 54.78 square units</u>

8 0
3 years ago
75 is what percentage of 50?
Alex17521 [72]

Answer:

ok the last one is 25%

the third one is 10%

second one is 50%

first one is 37.5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the GCF of the monomials: 72x^3 y^2 and 210x^2y^5
denpristay [2]

Answer: The GCF of the monomials is 1.

4 0
4 years ago
Read 2 more answers
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