SOLUTION: A function is given: f(x)=3x+12 a. Determine the inverse of this function and name it g(x). b. Use composite functions to show that these functions are inverses. c. Evaluate f

Algebra ->  Radicals -> SOLUTION: A function is given: f(x)=3x+12 a. Determine the inverse of this function and name it g(x). b. Use composite functions to show that these functions are inverses. c. Evaluate f      Log On


   

Question 1069948: A function is given: f(x)=3x+12
a. Determine the inverse of this function and name it g(x).
b. Use composite functions to show that these functions are inverses.
c. Evaluate f(g(-2)). Explain: What is the domain?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=3x%2B12
Interchange x and y,
x=3y%2B12
Solve for y.
3y=x-12
y=%28x-12%29%2F3
This new y is the inverse of the original function,
g%28x%29=%28x-12%29%2F3
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.
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f%28g%29=3g%2B12=3%28%28x-12%29%2F3%29%2B12=x-12%2B12=x
g%28f%29=%28f-12%29%2F3=%283x%2B12-12%29%2F3=%283x%29%2F3=x
f and g are inverses.
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.
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f%28g%28-2%29%29=-2
As shown in b.
Domain is all real numbers.
Range is all real numbers.