Find the inverse of f(x) = 3x + 6, and the domain and range of f(x) and `f^-1(x)` .

Expert Answers

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The function f(x) = 3x + 6.

First, find the inverse function `f^-1(x)`

y = f(x) = 3x + 6

=> 3x = y - 6

=> x = (y - 6)/3

interchanging x and y gives y = (x - 6)/3

=> `f^-1(x) = (x - 6)/3`

f(x) = 3x + 6 has real values for all values of x lying in R. The domain of the function is R. Also, f(x) can take all values in R for x lying in R. Similarly, it can be seen that (x - 6)/3 gives a real value for all real values of R. And (x - 6)/3 can take all values in R if x is real. Therefore the range and domain of both f(x) and `f^-1(x)` is R.

The inverse `f^-1(x) = (x - 6)/3` . The range and domain of f(x) and `f^-1(x)` is R

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