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

[tex]f(x)=x^2-16[/tex]

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

Answer Link

johanrusli johanrusli · Answer 2 · 2019-07-06T11:54:44+02:00

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!

[tex]f(x) = x^2 - 16[/tex]

[tex]y = x^2 - 16[/tex]

[tex]y + 16 = x^2[/tex]

[tex]x = \pm \sqrt{y + 16}[/tex]

[tex]f^{-1}(x) = \begin{cases} & \sqrt{x + 16} \text{ if } y \geq 0 \\ & -\sqrt{x + 16}\text{ if } y < 0 \end{cases}[/tex]

Learn more

Inverse of Function : https://brainly.com/question/9289171
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Graph of Function : https://brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic