Question

Two piecewise functions are shown below.

h(x)

-3x for x < 2

4x + 1 for x >= 2

g(x)

x^2 + 2 for x < 3

x^3 for x>= 3

What is the value of 3h(2) + 4g(1)?

Answer 1

To calculate 3h(2) + 4g(1), apply the correct part of each piecewise function based on the given inputs and then use algebra to find the sum. The result is -6.

Step-by-step explanation:

To calculate the expression 3h(2) + 4g(1), we must first determine which part of the piecewise functions to use for each given input. Since 2 is less than 3, for h(x) we'll use -3x and for g(x) we'll use x2 + 2.

First, find h(2):
h(2) = -3(2) = -6

Then, find g(1):
g(1) = 12 + 2 = 1 + 2 = 3

Now multiply each function value by the respective coefficients:
3h(2) = 3(-6) = -18 and 4g(1) = 4(3) = 12

Lastly, add the two results together to get the final answer:
3h(2) + 4g(1) = -18 + 12 = -6.