f(x)=2x-1 and g(x)=3x-4
Answer (1)
Answer: Functions:()=2−1f(x)=2x−1 and ()=3−4g(x)=3x−4 are both linear.• Slopes: =2mf =2, =3mg =3.• y-intercepts: (0)=−1f(0)=−1, (0)=−4g(0)=−4.Sum/Difference/Product/Quotient:(+)()=5−5(f+g)(x)=5x−5 — add coefficients and constants.(−)()=−+3(f−g)(x)=−x+3 — subtract term by term.()()=(2−1)(3−4)=62−11+4(fg)(x)=(2x−1)(3x−4)=6x2−11x+4.(/)()=2−13−4(f/g)(x)=3x−42x−1 , defined for ≠43x=34 .Compositions:(())=2(3−4)−1=6−9f(g(x))=2(3x−4)−1=6x−9.(())=3(2−1)−4=6−7g(f(x))=3(2x−1)−4=6x−7.Short explanation: substitute one function’s formula into the other.Intersection (solve ()=()f(x)=g(x)):2−1=3−4⇒=32x−1=3x−4⇒x=3. Then (3)=(3)=5f(3)=g(3)=5.Short explanation: set the lines equal to find where they cross.Inverses:−1()=+12f−1(x)=2x+1 , −1()=+43g−1(x)=3x+4 .Step-by-step explanation: swap x and Then solve for y.
