Which of the following is true for the relation f(x) = 2x2 + 1? only the equation is a function. neither the equation nor its inverse is a function. both the equation and its inverse are functions. only the inverse is a function.

Both the equation and its inverse are functions.

Step-by-step explanation:

Since, a relation is called a function when an input value of the relation has only one output value,

Here, the given relation,

When we plot the graph of this function,

We observed that all vertical line intersects the graph exactly once, except

, x = 0,

Thus, by vertical line test,

In the given equation every x has only one output value,

⇒ f(x) is a function,

Now, the inverse of a function is also a function,

⇒ is also a function,

Hence, Both the equation and its inverse are functions.

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..