[tex](g-f)(x) = -x^2-5x-5[/tex]
Step-by-step explanation:
Given functions are:
[tex]f(x) = x^2+6x-2\\g(x) = x-7\\h(x) = x+4[/tex]
The operations on functions can be performed just as they are performed on polynomials
So
[tex](g-f)(x)=g(x)-f(x)\\=(x-7)-(x^2+6x-2)\\=x-7-x^2-6x+2\\[/tex]
Combining like terms
[tex]=-x^2+x-6x-7+2\\=-x^2-5x-5[/tex]
Hence,
[tex](g-f)(x) = -x^2-5x-5[/tex]
Keywords: Functions
Learn more about functions at:
- brainly.com/question/2821386
- brainly.com/question/2860697
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