SOLUTION: Let f(x)=x^2,g(x)=2x-3 a)Find (f+g)(2)= b)Find the domain of (f/g)(x) c)Find the range of f+g

Algebra ->  Coordinate-system -> SOLUTION: Let f(x)=x^2,g(x)=2x-3 a)Find (f+g)(2)= b)Find the domain of (f/g)(x) c)Find the range of f+g       Log On


   

Question 1128469: Let f(x)=x^2,g(x)=2x-3
a)Find (f+g)(2)=
b)Find the domain of (f/g)(x)
c)Find the range of f+g
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let
f%28x%29=x%5E2
g%28x%29=2x-3
a)
Find %28f%2Bg%29%282%29=f%282%29%2Bg%282%29=2%5E2%2B2%2A2-3=4%2B4-3=8-3=5
b)
Find the domain of %28f%2Fg%29%28x%29=f%28x%29%2Fg%28x%29=x%5E2%2F%282x-3%29
denominator cannot be equal to zero, so exclude value of x which makes it equal to zero
2x-3=0=>x=3%2F2
so, the domain: { x elememt R: x%3C%3E3%2F2
c)
Find the range of f%2Bg
f%2Bg=x%5E2%2B2x-3-> it's upward parabola,has minimum ;so, write it in vertex form
f%2Bg=%28x%5E2%2B2x%2Bb%5E2%29-b%5E2-3
f%2Bg=%28x%5E2%2B2x%2B1%5E2%29-1%5E2-3
f%2Bg=%28x%2B1%29%5E2-4 => vertex (minimum) is at (1,-4)
so, the range is :
{ y element R : y%3E=-4 }