Need help with function problem

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The discussion focuses on the composition of functions, specifically finding g(f(x)) where f(x) = 3x + 1 and g(x) = (x^2 + 5x)^-1/2. The correct substitution involves replacing x in g with the expression for f, resulting in g(f(x)) = (9x^2 + 21x + 6)^-0.5. The final expression confirms the accuracy of the calculations presented.

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If f(x) = 3x + 1
and g(x) = (x^2 + 5x)^-1/2
find g(f(x))
 
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Does this look right?

f(x) = 3x + 1
g(b) = (b^2 + 5b)^-1/2
Let b=f(x)=3x+1
Substitute 3x + 1 in for b:
g(b)=((3x+1)^2+5* (3x+1))^-.5
=(9x^2+6x+1+15x+5)^-.5
=(9x^2+21x+6)^-.5
g(f(x))= (9x^2+21x+6)^-.5
Please advise
 
Yes, that's exactly right. To find g(f(x)) you replace the "x" in the formula for g with the formula for f(x).
 

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