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.

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squirreleats squirreleats · Answer 1 · 2017-10-15T23:58:30+02:00

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

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slicergiza slicergiza · Answer 2 · 2019-06-29T12:34:10+02:00

Answer:

Both the equation and its inverse are functions.

Step-by-step explanation:

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

Here, the given function,

[tex]f(x)=5x+1[/tex]

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

[tex]y = \frac{1-x}{-5}=\frac{x-1}{5}[/tex]

Replace y by [tex]f^{-1}(x)[/tex],

[tex]f^{-1}(x)=\frac{x-1}{5}[/tex]

Which is also a polynomial,

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

Last option is correct.