Option A
If f(x) = [tex]2x^2 + 1[/tex] and g(x) = [tex]x^2 - 7[/tex] then [tex](f - g)(x) = x^2 + 8[/tex]
Solution:
Given that f(x) = [tex]2x^2 + 1[/tex] and g(x) = [tex]x^2 - 7[/tex]
To find: (f - g)(x)
We know that,
(f – g)(x) = f (x) - g(x)
Let us substitute the given values of f(x) and g(x) in above formula,
[tex](f - g)(x) = 2x^2 + 1 - (x^2 - 7)[/tex]
For solving the brackets in above expression,
There are two simple rules to remember:
When you multiply a negative number by a positive number then the product is always negative.
When you multiply two negative numbers or two positive numbers then the product is always positive.
So the expression becomes,
[tex](f - g)(x) = 2x^2 + 1 -x^2 + 7[/tex]
Combining the like terms,
[tex](f - g)(x) = 2x^2 - x^2 + 1 + 7\\\\(f - g)(x) = x^2 + 8[/tex]
Thus option A is correct
