Need help with function problem

Thread starter Aprilshowers
Start date Jul 13, 2005
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Function

AI Thread Summary

To find g(f(x)), substitute f(x) = 3x + 1 into g(x) = (x^2 + 5x)^-1/2. This results in g(f(x)) = ((3x + 1)^2 + 5(3x + 1))^-1/2, which simplifies to (9x^2 + 21x + 6)^-1/2. The calculations are confirmed to be correct, demonstrating the proper method of function composition. The final expression for g(f(x)) is indeed (9x^2 + 21x + 6)^-1/2.

Jul 13, 2005

Aprilshowers

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

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Jul 13, 2005

Aprilshowers

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

Jul 13, 2005

HallsofIvy

Science Advisor

Homework Helper

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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