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

1 Answer
Oct 6, 2017

Answer:

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)#