Question

A particular function takes an input, squares it and then adds 1 to the new value to complete the output. What are possible inputs and outputs of this function?

Answer 1

Input values include all real values. Output values are all numbers greater than or equal to 1.

Explanation:

Let the input be 'x' and output of the given function be 'y'.

A function is just like a machine that gives an output for a given input.

The input to a function is called the domain of a given function. The output of a function is called its range.

The variable that is used to represent the domain is 'x' and the range is represented by the variable 'y'.

So, the domain is the independent variable and range depends on the values of the domain.

Given:

The square of input and adding 1 to the square gives the output.

Framing in equation form, we get:

`y=x^2+1`

Now, the input can be any real number as the square of any ream number is defined without any restriction.

Therefore, the possible values of the input 'x' is all real numbers.

Now, the value of
`x^2` is always a positive number with 0 being its minimum value.

Now, for the output, 1 is added to
`x^2`, so the minimum value of output is 0 + 1 = 1.

Now, adding a positive number to another positive number yields in positive number as the result.

Therefore, the output values include all positive values greater than or equal to 1.