Evaluate the function at the specified value of the independent variable and simplify.
f(x) = (2x^2 + 8x)/(5x^3 + 40) at x =
3.
wherever there is an x, plug in a 3 and then simplify:
f(3) = (2*3^2 + 8*3)/(5*3^3 + 40)
= (18+24)/(135+40)
= 42/175
= 6/25
To evaluate the function f(x) at x = 3, we need to substitute 3 in place of x in the function and simplify the expression.
f(x) = (2x^2 + 8x)/(5x^3 + 40)
Replacing x with 3, we get:
f(3) = (2(3)^2 + 8(3))/(5(3)^3 + 40)
Now, we simplify the expression within the parentheses and calculate the values:
f(3) = (2(9) + 8(3))/(5(27) + 40)
= (18 + 24)/(135 + 40)
= 42/175
So, f(3) = 42/175.
Therefore, the function evaluated at x = 3 simplifies to 42/175.