Answer:
The value of g(f(0)) is 36
Step-by-step explanation:
g(f(x)) is a composite function, where f(x) is the value of x in g(x), which means substitute x in g(x) by f(x)
Let us use this rule to solve our question
∵ f(x) = -x + 9
∵ g(x) = x² - 6x + 9
→ Substitute x in g by f
∵g(f(x)) = g(-x + 9)
∴ g(f(x)) = (-x + 9)² - 6(-x + 9) + 9
→ Let us simplify it
∵ (-x + 9)² = (-x)(-x) + (-x)(9) + (9)(-x) + (9)(9)
∴ (-x + 9)² = x² + -9x + -9x + 81
→ Add the like terms (-9x + -9x)
∴ (-x + 9)² = x² + -18x + 81
→ Remember (+)(-) = (-)
∴ (-x + 9)² = x² - 18x + 81
∵ - 6(-x + 9) = -6(-x) + (-6)(9)
∴ - 6(-x + 9) = 6x + -54
∴ - 6(-x + 9) = 6x - 54
→ Substitute them in g(f(x))
∴ g(f(x)) = x² - 18x + 81 + 6x - 54 + 9
→ Add the like terms
∴ g(f(x)) = x² + (-18x + 6x) + (81 -54 + 9)
∴ g(f(x)) = x² + (-12x) + (36)
∴ g(f(x)) = x² - 12x + 36
→ Now substitute x by 0
∴ g(f(0)) = (0)² - 12(0) + 36
∴ g(f(0)) = 0 - 0 + 36
∴ g(f(0)) = 36
There is an easy way to find it quickly
Substitute x in f by 0
f(0) = -(0) + 9
f(0) = 9
Substitute x in g by 9
Find g(9)
g(9) = (9)² - 6(9) + 9
g(9) = 81 - 54 + 9
g(9) = 36
