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anyanavicka [17]
3 years ago
12

Inverse function details

Mathematics
1 answer:
Lerok [7]3 years ago
5 0

Step-by-step explanation:

First, replace f(x) with y ⇒ f(x)=6x-19 ⇒ y=6x-19

Then y with x and x with y  ⇒ y=6x-19 ⇒ x=6y-19

Solve the equation from for y:

           x=6y-19

           x+19=6y dividing with 6

           1/6 x +(19/6) = y

Replace y with f−1(x) ⇒ f−1(x)= 1/6 x +(19/6)

hope this helps!

           

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Make the indicated trigonometric substitution in the given algebraic expression and simplify(x-25)/x = Sin y0
Strike441 [17]

Answer:

x = 25 /(1 − sin(y )) and y ≠ π/2  +2πn

Step-by-step explanation:

Let's solve and simplify for x,

(x − 25 )/ x  = sin(y)

Let's multiply both sides by x

((x − 25 )/x) *x= sin(y)*x

Then,

x − 25 = sin(y) * x

Let's add 25 to both sides

x − 25 + 25 = sin(y) * x + 25

If simplify again,

x = sin(y) * x + 25

Then we need subtract sin y x from both sides

x − sin(y) * x = sin (y)* x + 25 − sin (y)* x

It will equal:

x − sin (y)* x = 25

Factor x−sin(y) x: x(1−sin(y) ), then we get:

x (1 − sin(y)) = 25

Finally we need divide both sides by 1 − sin(y) ; y ≠π /2 + 2πn

And it will give us this equation:

x = 25 /(1 − sin(y )) and y ≠ π/2  +2πn

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