For the function find f-1(x)

Mathematics

2 answers:

Svetach [21]2 years ago

8 0

The answer is C. i know because i looked it up

Mkey [24]2 years ago

6 0

since you know that to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solve for "y".

$\stackrel{f(x)}{y}=\sqrt[3]{\cfrac{x+6}{2}}\implies \stackrel{\textit{quick switcheroo}}{x=\sqrt[3]{\cfrac{y+6}{2}}}\implies \stackrel{\textit{cubing both sides}}{x^3=\cfrac{y+6}{2}} \\\\\\ 2x^3=y+6\implies 2x^3-6=\stackrel{f^{-1}(x)}{y}$

You might be interested in

If csc ( x ) = 4, for 90 ∘ < x < 180, then sin ( x 2 ) = ? cos ( x 2 ) = ? tan ( x 2 ) = ?

svetlana [45]

Answer:

I'm assuming where you wrote x2, you meant 2x.

Anyway, if csc (x) = 2, since csc(x) = 1/sin(x), we know that 1/sin x = 2, so sin (x) = 1/2. Since sin2x + cos2x = 1, cos2x = 1 - sin2x, so cos x = √1 - sin2x. In this case, cos x = √ 1 - (1/2)2 = √(3/4) = (√3)/2. Finally, since sin x = opp / hyp , cos = adj/ hyp: sin x / cos x = (opp/hyp)/(adj/hyp) = opp/adj = tan x. So this means that tan x = sin x / cos x = 1/2 / √ 3 / 2 = 1/√3 = √3 / 3

At this point, all that is necessary is to use the double angle formulas for sin, cos, and tan.

sin (2x) = 2 sin x cos x = 2 (1/2) (√3/2) = √3 / 2

cos (2x) = cos2x - sin2x = (√3/2)2 - (1/2)2 = 3/4 - 1/4 = 1/2

tan (2x) = 2 tan x / (1 - tan2x) = 2 (√3 / 3) / ( 1 - (√3/3)2) = 2/√3 / (1 - 1/3) = 2/√3 / (2/3) = 3/√3 = √3

To sum up, sin (2x) = √4 / 2, cos (2x) = 1/2, and tan(2x) = ✓3.

Step-by-step explanation:

BRAIN LY FAST

MARK A BRAINLESS

5 0

2 years ago

Help me Please..

Fittoniya [83]

Just general definitons:

a TRInomial has 3 terms (tri means three)
a BInomial has 2 terms (bi means two)
a MONOmial has 1 term (mono means one)

the degree is the highest exponent found in the algebraic expression

so they should be pretty easy to solve with that information, but just in case:

1. trinomial, degree of 4
2. binomial, degree of 3
3. monomial, degree of 2

for the final question, all you have to do is plug in 2 for x, so

(2)^2 - 2(2) + 1

4 - 4 + 1

so the answer is 1

7 0

3 years ago

Please help me! Will give brainlst :)

Sati [7]

Answer:

Step-by-step explanation: