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Need help with function problem

If f(x) = 3x + 1
and g(x) = (x^2 + 5x)^-1/2
find g(f(x))
 
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
 

HallsofIvy

Science Advisor
Homework Helper
41,682
864
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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