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.

2

step-by-step explanation: