Question

The inverse of f(x)=9x^2

Answer 1

f-¹(x) = √(x)/3

Explanation:

Now we have to,

→ find the inverse of f(x)=9x²

Then the inverse function will be,

→ f(x) = 9x²

→ y = 9x²

→ 9y² = x

→ y² = x/9

→ y = √(x/9)

→ [ y = √(x)/3 ]

Hence, the inverse is √(x)/3.

Answer 2

Given function:

• f(x) = 9x²

Let the inverse is y = f⁻¹(x).

Swap x and y in the given function and solve for y:

• x = 9y²
• y² = x/9
• y = √(x/9)
• y = √x / 3

The inverse of the given function is:

• f⁻¹(x) = √x / 3