Question

If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?

Answer 1

Answer:

  68

Step-by-step explanation:

Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.

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f∘g

The "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.

Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.

g(-2)

To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...

  g(x) = 5x +4

  g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math

f(g(-2))

Now that we know g(-2) = -6, we know this expression is ...

  f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x

Then the value we're looking for is ...

  (f∘g)(-2) = 68