If f(x) = x² -16 , then f⁻¹(x) = ± √ ( x + 16 )
Further explanation
Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
- Linear Function → f(x) = ax + b
- Quadratic Function → f(x) = ax² + bx + c
- Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
- Logarithmic function → f(x) = ln x
- Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...
If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!
\(f(x) = x^2 - 16\)
\(y = x^2 - 16\)
\(y + 16 = x^2\)
\(x = \pm \sqrt{y + 16}\)
\(f^{-1}(x) = \begin{cases} & \sqrt{x + 16} \text{ if } y \geq 0 \\ & -\sqrt{x + 16}\text{ if } y < 0 \end{cases}\)
Learn more
- Inverse of Function : https://brainly.com/question/9289171
- Rate of Change : https://brainly.com/question/11919986
- Graph of Function : https://brainly.com/question/7829758
Answer details
Grade: High School
Subject: Mathematics
Chapter: Function
Keywords: Function , Trigonometric , Linear , Quadratic
