Question

Which of the following is true for the relation f(x) = 5x + 1?

Only the inverse is a function.


Only the equation is a function.


Neither the equation nor its inverse is a function.


Both the equation and its inverse are functions.

Answer 1

I think both of them are function if you draw them you will find out that and always the polynomials first degree is functions.

Answer 2

Both the equation and its inverse are functions.

Explanation:

A function is relation in which one input gives one and only one output.

Here, the given function,

`f(x)=5x+1`

Which is a polynomial,

A polynomial is a function because for each input value it gives only one output value.

⇒ f(x) is a function.

Now, For finding the inverse of f(x),

Replace f(x) by y,

y = 5x + 1

Switch x and y,

x = 5y + 1

Isolate y on the left side,

-5y = 1 - x

`y = (1-x)/(-5)=(x-1)/(5)`

Replace y by
`f^(-1)(x)`,

`f^(-1)(x)=(x-1)/(5)`

Which is also a polynomial,

Hence, the inverse of f(x) is also a function,

Last option is correct.