Given the definitions of f(x) and g(x) below, find the value of g(f(0)) f(x)= -x+9
g(x)=x^2 - 6x+9

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

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation: