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horrorfan [7]
3 years ago
13

F(x) = 1/x+5, g(x) = 5x+1/x

Mathematics
1 answer:
amm18123 years ago
4 0
We have
f(x) = 1/x+5,
g(x) = 5x+1/x -------> (5x²+1)/x
<span>
1) find the f(g(x))
</span>f(g(x))=(1/(5x²+1)/x) +5---- > (x/(5x²+1)) +5---->(x+5*(5x²+1))/(5x²+1)
(x+25x²+5)/(5x²+1)---------- > (25x²+x+5)/(5x²+1)

f(g(x))= (25x²+x+5)/(5x²+1)--------> is not x

therefore
<span>f(x) and g(x) are not inverses of each other

</span>the domain of the composition f(g(x)) is (-∞,∞)

2) find the g(f(x))
g(f(x))=(5(1/x+5,)²+1)/(1/x+5,)------- > (5/x²)+(10/x)+25+(x/(5x+1))
[5*(5x+1)+10x*(5x+1)+25x²*(5x+1)+x³]/[x²*(5x+1)]

the domain of the composition g(f(x)) is (-∞, -1/5) U (-1/5,0) U (0,∞)



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