4) If g(x)= 3x-5 and h(x)= 2x–4 then (goh)(x) is 6x - 17
5) The composite function f(g(x)) is x² + 8x + 21
A function inside another function is known as composite function
Given the following functions
g(x)= 3x-5
h(x)= 2x–4
(goh)(x)= g(h(x))
g(h(x)) = g(2x - 4)
g(2x-4) = 3(2x-4)-5
g(2x-4) = 6x - 12 - 5
g(2x-4) = 6x - 17
Hence (goh)(x) is 6x - 17
5) Given the functions
f(x)=x² +5 and g (x) = x +4
f(g(x)) = f(x+4)
f(x+4) = (x+4)² + 5
Expand
f(x+4) = x² + 8x +16 + 5
f(x+4) = x² + 8x +21
Hence the composite function f(g(x)) is x² + 8x + 21
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