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18 hours ago

Which function has an inverse that is also a function?

Mathematics

2 answers:

PIT_PIT [9.1K]18 hours ago

4 0

Option C has an inverse that is indeed a function

{ ( -1, 3 ), ( 0,4 ), ( 1, 14 ), ( 5, 6 ), ( 7, 2 )}

To elaborate

A function represents a relation where each element from the domain corresponds to one element in the codomain.

There are various classifications 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 +...

For a function f: x → y, the inverse is denoted f⁻¹: y → x

Let's now address the task!

Based on the previously mentioned definition, it can be inferred that a function cannot have identical x values.

Among the four provided tables, option C presents a function whose inverse is also functional. This results from having unique x and y values throughout.

$\{(-1,3), ( 0,4} ), ( 1,14 ), ( 5, 6), ( 7, 2) \}$

Option A lacks an inverse due to repeated y value(s), for instance, 4

$\{(-1,-2), ( 0,\boxed{4} ), ( 1,3 ), ( 5, 14), ( 7, \boxed {4}) \}$

Option B does not have an inverse either, also because of y value repetition, specifically 4

$\{(-1,-2), ( 0,\boxed{4} ), ( 1,5 ), ( 5, \boxed {4}), ( 7, 2) \}$

Option D fails to maintain an inverse as y values are repeated, like 4

$\{(-1,\boxed {4}), ( 0,\boxed{4} ), ( 1,2 ), ( 5, 3), ( 7, 1) \}$

Discover more

Inverse of Function:
Rate of Change:
Graph of Function:

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function, Trigonometric, Linear, Quadratic

Leona [9.2K]18 hours ago

3 0

An inverse function will also qualify as a function if the original is a One-to-One function. This means that each y value corresponds to exactly one x value, thus ensuring that the inverse remains a function.

The function shown in option C meets this criteria, as all x values and y values are distinct. Therefore, the inverse of the function in option C will also be a functional relation.

In contrast, other options have repeated y values, indicating they do not exhibit the one-to-one characteristic.

Hence, the correct answer is option C

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