Correct answer is C). 6X+11
Step-by-step explanation:
The given function f(x)= [tex]\frac{24x^{2} +63x + 34 }{4x+3}[/tex]
On simplying the function f(x),
f(x)= [tex]\frac{6x(4x+3) -18x +63x + 34 }{4x+3}[/tex]
f(x)= [tex]\frac{6x(4x+3) +45x + 34}{4x+3}[/tex]
f(x)= [tex]\frac{6x(4x+3) +11(4x+3)+x-33 + 34 }{4x+3}[/tex]
f(x)= [tex]\frac{6x(4x+3) +11(4x+3)+x+1}{4x+3}[/tex]
f(x)=[tex](6x+11)+\frac{(x+1)}{4x+3}[/tex]
From above equation
"(6x+11)" is Oblique asymptote and [tex]\frac{(x+1)}{4x+3}[/tex] is vertical asymptote
Therefore, Correct answer is C). 6X+11
