[tex](fog)(7) = -6[/tex]
Step-by-step explanation:
The function composition is achieved by putting the second function in first function in place of independent variable.
Given functions are:
[tex]f(x) = -5x-1\\g(x) =\sqrt{x-6}[/tex]
In order to find (fog)(x) we will put function g in function f in place of x
[tex](fog)(x) = -5(g(x)) -1\\= -5\sqrt{x-6}-1[/tex]
Since we have to find (fog)(7)
Putting 7 in place of x
[tex]= -5\sqrt{7-6} - 1\\=-5\sqrt{1}-1\\= -5(1) -1\\= -5-1\\=-6[/tex]
Hence,
[tex](fog)(7) = -6[/tex]
Keywords: Functions, composition
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