Horizontal Asymptotes and Functions

1. If f(x)= 1/(2x + 3), then [f (1 + h) - f(1)]/h is ?
2. If f(x)=x2 + x4 and g(x)= square root (x-1), then (f o g)(x) is?
3. Identify the vertical and horizontal asymptotes of the given function y = g(x) = 3/(3x-1)

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/algebra/horizontal-asymptotes-and-functions-2t4
Attachments

Solution Preview

.../(3x-1)

Solution:

1. f(x)= 1/(2x + 3), thus

f(1+h)= 1/(2(1+h) + 3)=1/(5+2h)
f(1)= 1/(2 + 3)=1/5

Thus

[f (1 + h) - f(1)]/h =[1/(5+2h)- 1/5]/h ( Note common denominator is (5+2h)5 )

=[5-(5+2h)]/[(5+2h)5h]=-2h/[(5+2h)5h]= ...