The domain for f(x) and g(x) is all real numbers. Let f(x) = 3x^2 + x-7 and g(x) = x^2 + 4x-5 Find (f-g)(x). SHOW WORK PLEASE

Answer: [tex](f-g)(x) =  2x^{2}  - 3x -2[/tex]Step-by-step explanation:Here, the given functions are:[tex]f(x) = 3x^{2}  + x -7\\g(x) = x^{2} + 4x - 5[/tex]Now, as both the functions are POLYNOMIAL, and POLYNOMIAL FUNCTION FOLLOW THE  LINEAR TRANSFORMATION.⇒(f-g)(x) = f(x) - g(x) Now ,  [tex]f(x) - g(x)  = 3x^{2}  + x -7 -(x^{2} + 4x - 5)\\   =  3x^{2}  + x -7 - x^{2}  - 4x+5[/tex]= [tex](3x^{2}  - x^{2})  + (x  - 4x)  -7  +5  = 2x^{2}  - 3x -2[/tex] [tex]\implies f(x) - g(x) =  2x^{2}  - 3x -2[/tex]Or,   [tex](f-g)(x) =  2x^{2}  - 3x -2[/tex]