Restrict the domain of the quadratic function and find its inverse. confirm the inverse relationship using composition. f(x) = 0.2x2 the domain is (x| x ). since f−1f(x) = x for x 0, it has been confirmed that f−1(x) = for x ≥ 0 is the inverse function of f(x) = 0.2x2 for x 0. chose the graph of the function and its inverse.

The given function is

f(x)= 0.2 x²

Since f(x) will be defined for all real values of x.

So, Domain of f(x) will be ( x| x is a real number.)→This is set builder notation.

Finding the inverse of f(x):

y = 0.2 x²

→ x²= 5 y

→x = → → Inverse of f(x)

Replacing x by y and y by x,we get inverse of the given function

y = → →Domain x ≥ 0, x∈[0,∞]

Graph of function and its inverse are shown below.

Domain = {x | x≥0 }

Inverse = f⁻¹(x) = .

Step-by-step explanation:

The given function is

We know that the domain of all functions is the whole real line.

But as .

So, the domain of f(x) is the positive real line.

Thus, the restriction to the domain of f(x) is {x | x≥0 }.

Now, we will find the inverse of f(x),

i.e.

i.e.

i.e.

Hence, the inverse of f(x) is f⁻¹(x) = .

Further, we will check the inverse using composition rule.

i.e. fοf⁻¹(x) = f⁻¹οf(x)

i.e. f(f⁻¹(x)) = f⁻¹(f(x))

i.e. f() = f⁻¹()

i.e. =

i.e. 0.2 × 5x =

i.e. x = x

Hence, we get that the function has inverse f⁻¹(x) = .

The graph of the function and its inverse can be seen below.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841