Final answer:
To find the vertical asymptotes of the function f(x)=(2ˣ²+30x+¹⁰⁸¹)/(4ˣ²-9), we set the denominator equal to zero and solve for x, giving us x = 1/2 and x = -1/2.
Step-by-step explanation:
The function is given by f(x) = (2ˣ²+30x+¹⁰⁸¹)/(4ˣ²-9).
To find the vertical asymptotes, we need to look for values of x that make the denominator of the fraction zero. In this case, the denominator is 4ˣ²-9. Setting this equal to zero and solving for x, we get 4ˣ² = 9, which gives us 2 solutions: x = 1/2 and x = -1/2.
So, the vertical asymptotes of the function f(x) = (2ˣ²+30x+¹⁰⁸¹)/(4ˣ²-9) are x = 1/2 and x = -1/2.