Question

How do you find the domain and range of `f(x)=7x^2-11x+9`?

Answer 1

See explanation.

Explanation:

The function is a polynomial, so its domain is `RR`.

To find the range we have to find the coordinates of the vertex of parabola.

`p=(-b)/(2a)`

`p=11/(2*7)=11/14`

To calculate `q` we can either use the formula:

`q=(-Delta)/(4a)`

Or calculate the value of `f(p)` by substituting `p` for `x`:

`q=f(p)=7*(11/14)^2-11*(11/14)+9`

`q=847/196-121/14+9`

`q=(847-1694+1764)/196`

`q=917/196`

`q=4 133/196`

The coefficient of `x^2` is positive, so the range is:

`r=[4 133/196;+oo)`