Question

If f(x) = x-5 and g(x) = x² - 1, find (f - g)(x - 1)

Answer 1

Given the following

f(x) = x-5

g(x) = x^2-1

(f-g)(x) = f(x) - g(x)

Substitute the given function into the expression

(f-g)(x) = x-5 - (x² - 1)

(f-g)(x) = x-5-x²+1

(f-g)(x) = -x²+x-4

if x = -1, substitute x = -1 into the resulting function

(f-g)(-1) = -(-1)²+(-1)-4

(f-g)(-1) = -1-1-4

(f-g)(-1) = -6

Hence the value of the expression given is -6