Question

Which function has an inverse that is also a function?

Answer 1

Option C has an inverse that is also a function

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

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!

According to the definition above, it can be concluded that a function cannot have the same x value.

Of the four tables available in choices, table option C has an inverse that is also a function. This is because x values and y values are all different.

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

Option A doesn't have inverse because there is the same value of y i.e 4

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

Option B doesn't have inverse because there is the same value of y i.e 4

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

Option D doesn't have inverse because there is the same value of y i.e 4

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

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

Answer 2

The inverse of a function will also be a function if it is a One-to-One function. This means, if each y value is paired with exactly one x value then the inverse of a function will also be a function.

Option C gives us such a function, all x values are different and all y values are different. So inverse of function given in option C will result in a relation which will also be a function.

In all other options, y values are being repeated, which means they are not one to one functions.

So, the answer to this question is option C