Question

Given the definitions of f(x) and g(x) below, find the value of (fog)(-1).

f(x) =-x-12
g(x) = x² – 5x -5

Answer 1

Answer: 11

Step-by-step explanation: To find the value of (fog)(-1), we first need to find the value of g(-1), which means plugging -1 into the equation for g(x):

g(x) = x² – 5x - 5

g(-1) = (-1)² – 5(-1) - 5

g(-1) = 1 + 5 - 5

g(-1) = 1

Now we need to find (fog)(x) by plugging g(x) into f(x) and simplifying:

f(x) = -x - 12

fog(x) = f(g(x))

fog(x) = f(x² – 5x - 5)

fog(x) = -(x² – 5x - 5) - 12

fog(x) = -x² + 5x + 17

Finally, we can find (fog)(-1) by plugging -1 into the equation for fog(x):

fog(x) = -x² + 5x + 17

(fog)(-1) = -(-1)² + 5(-1) + 17

(fog)(-1) = -1 - 5 + 17

(fog)(-1) = 11

Therefore, the value of (fog)(-1) is 11.