(f-g)(x) = x^2 + 7
(f-g)(x) = f(x) - g(x)
2x^2 - x^2 - 2 = x^2 + 7
The value of (f-g)(x) is [tex]x^2+7[/tex]. This is obtained by using operations on function(subtraction operation).
Consider two functions f(x) and g(x)
Then,
Addition: (f+g)(x) = f(x)+g(x)
Subtraction: (f-g)(x) = f(x)-g(x)
Multiplication: (f×g)(x)=f(x) × g(x)
Division:(f/g)(x) = f(x)/g(x)
The given functions are f(x) = [tex]2x^2+5[/tex] and g(x)= [tex]x^2 -2[/tex]
Thus, from the operations on functions we know that,
(f-g)(x) = f(x) - g(x)
So,
(f-g)(x) = [tex](2x^2+5) - (x^2 -2)[/tex]
= [tex]2x^2+5 - x^2 + 2[/tex]
= [tex]x^2 + 7[/tex]
Therefore, for the functions f(x) = [tex]2x^2+5[/tex] and g(x)= [tex]x^2 -2[/tex], the value of (f-g)(x) is [tex]x^2+7[/tex].
Learn more about operations on functions here:
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