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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.

2 Answers

1 vote
I think both of them are function if you draw them you will find out that and always the polynomials first degree is functions.
User Mike Cornell
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7.9k points
3 votes

Answer:

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.

User Volni
by
7.4k points

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