Question 839476
To find f(1), we need to first find k in our function.  We do this by replacing each of our x's with -3 and setting that equal to -120:


(-3)^4 + (-3)^3 - 19(-3)^2 + k(-3) + 30 = -120 ----->


81 + (-27) - 19(9) - 3k + 30 = -120 ----->


81 - 27 - 171 - 3k + 30 = -120 ----->


-3k - 87 = -120


Next, we will add 87 to both sides of our equation, which will give us:


-3k = -33


Dividing both sides of our equation by -3 will give us the value of k:


k = 11


Now, we can replace k with 11 in our function and replace all of the x's with 1:


(1)^4 + (1)^3 - 19(1)^2 + (11)(1) + 30 ----->


1 + 1 - 19 + 11 + 30 ----->


24


Therefore, our answer is 24