f(x)=2x^2;g(x)=7-x (19) f(x)= -x^2;g(x)=3x (20) f(x)= 4x^2 -2x+1;g(x)= -5x (21)f(x)=2x^2;g(x)=7-x?

Question

let f(x0=x^2-1 and g(x)=2x-3. find each new function and write it in simplest form. Justify each step in the simplification, and state any domain restrictions?

Answer 1

Your question is not totally clear. Ithink your teacher is asking you to find f(g(x)). If so, then:

(18) f(x)=2x^2;g(x)=7-x
f(g(x)) = 2(7-x)^2 = 2(49-14x+x^2) = 98 - 28x+2x^2
No domain restrictions

(19) f(x)= -x^2;g(x)=3x
f(g(x)) = - (3x)^2 = -9x^2 No domain restrictions

(20) f(x)= 4x^2 -2x+1;g(x)= -5x
f(g(x)) = 2(-5x)^2 = = 50x^2 No domain restrictions

(21) f(x)=2x^2;g(x)=7-x
This is the same as problem 18

let f(x) =x^2-1 and g(x)=2x-3.
f(g(x)) = (2x-3)^2-1 = 4x^2-12x +3 -1 = 4x^2 -12x +2

If I wrong about what was wanted, I,m sorry.