Question

1S If f(x) = -x2 – 1, and g(x) = x + 5, then f(g(x)) = [ ? ]x2+[ ]x+[ ]

Answer 1

We are given:

f(x) = -x² - 1

g(x) = x + 5

Finding f(g(x)):

because g(x) = x+5

f(g(x)) = f(x+5)

f(x+5) = -(x+5)² - 1

f(x+5) = -(x² + 25 + 10x) - 1

f(x+5) = -x² - 25 - 10x - 1

f(x+5) = -x² - 10x - 26

comparing with the question,

first blank = (-1)

second blank = (-10)

third blank = (-26)