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4 years ago

Find the inverse function of F(x) = 2arccosx. F-1(x) = ____

Mathematics

1 answer:

Dmitriy789 [7]4 years ago

5 0

ANSWER

${f}^{ - 1} (x) = \cos( \frac{x}{2} )$

EXPLANATION

The given function is

$f(x) = 2 \arccos(x)$

Let

$y= 2 \arccos(x)$

Interchange x and y.

$x= 2 \arccos(y)$

Divide both sides by 2.

$\frac{x}{2} = \arccos(y)$

We take cosines to get,

$\cos( \frac{x}{2} ) = y$

${f}^{ - 1} (x) = \cos( \frac{x}{2} )$

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Please help with these questions

Elis [28]

Obviously, what you looking for is slopes. Now let's get started.
6.) 7x-5y=20 You subtract 7x both sides.
-7x -7x
-5y=-7x+20 Then you divide -5 both sides (which is include -7 and 20).
y=7/5x-4 Simplify.
-8x-3y=12 Add 8x both sides because it's a negative number.
+8x +8x
-3y=8x+12 Divide -3 both sides.
y=-8/3x-4 Simplify.
And your point value is (0,-4).
7.) -x-4y=12 Add x both sides.
+x +x
-4y=x+12 Divide -4 both sides.
y=-1/4x-3 Simplify.
20x+80y=0 Subtract 20x both sides.
-20x -20x
80y=-20x Divide 80 both sides. Here's a hint: 20/80 is same thing as 2/8, so
you don't have to do all that.
y=1/4x Simplify. Here's another hint: I bet you wondering there's no y- intercept. The y-intercept is (0,0).
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And your point value is (5,-1).
I hope it helps.

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