MATH SOLVE

3 months ago

Q:
# The function f(x) = 3x2 represents the altitude of a blimp, where x is the time in minutes. The function g(x) = −2x − 5 represents the time in minutes, where x is the height in thousands of feet of the blimp. What is the value of f[g(4)]? −507 −101 −13 507

Accepted Solution

A:

Answer:507Step-by-step explanation:The function which represents the altitude of blimp is:[tex]f(x)=3x^{2}[/tex]Here, x is the time in minutesThe function representing the time in minutes is:[tex]g(x)=-2x-5[/tex]Here, x is the height in thousands of feet of the blimp.We need to calculate f(g(4)). g(4) gives the time in minutes when the height is 4000 feet. So, f(g(4)) will give the altitude of the blimp when its height is 4000 feet.Substituting x = 4 in equation of g(x), we get:[tex]g(4) = -2(4) - 5 = -13[/tex]So,[tex]f(g(4))=f(-13)\\\\ =3(-13)^{2}\\\\ =3(169)\\\\ =507[/tex]Therefore, the value of f(g(4)) is 507