Question

Let f(x) = x2 - 16. Find f-1(x).

Answer 1

$f(x)=x^2-16$

To find $f^{-1}(x)$, (the inverse of the function) you need to first replace the f(x) with y...
$y=x^2-16$
Then switch the x and the y.
$x=y^2-16$
Solve for y.
$x+16=y^2$
Take the square root of each side...
$\boxed{y=\pm\sqrt{x+16}}$

Answer 2

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 : brainly.com/question/9289171
• Rate of Change : brainly.com/question/11919986
• Graph of Function : brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic