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function f(x) = 3x − 2 represents the altitude of a hot air balloon, where x is the time in minutes. The function g(x) = x2 − 1 represents the time in minutes, where x is the height in thousands of feet of the hot air balloon. What is the value of f[g(5)]?

168
70
34
24

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TaeKwonDoIsDead

Answer:

70

Step-by-step explanation:

" f[g(5)] " represents composition of a function. To evaluate this, we need to:

  • Plug in 5 into g(x), to find g(5), then
  • take that value and plug into f(x), to get final answer

First, g(5):

[tex]g(x)=x^2-1\\g(5)=(5)^2 -1\\g(5)=25-1\\g(5)=24[/tex]

Now we take "24" and substitute into f(x):

[tex]f(x)=3x-2\\f(24)=3(24)-2\\f(24)=72-2\\f(24)=70[/tex]

So,

f[g(5)] = 70

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