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]
