SOLUTION: what is the inverse of f(x)=10/5x+2? and what is the domain and rage for both f(x) and f^-1(x)?

Question 1092562: what is the inverse of f(x)=10/5x+2?
and what is the domain and rage for both f(x) and f^-1(x)?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

One version of the standard way to find the inverse of a function is to switch the x and y in the given function and solve for the new y.

In the given function, 0 is excluded from the domain because it would make the denominator 0. That means 0 is excluded from the range of the inverse function.

You can also see that 0 is not in the range of the inverse function, because if you try to solve

you get no solution.

Similarly you can see that 2 is excluded from the range of the given function, because, again, if you try to solve

you will get no solution. And since 2 is excluded from the range of the given function, it is excluded from the domain of the inverse function. And we can see that by looking at the inverse function, because x=2 would make the denominator 0.

In summary...

For the given function,
Domain is x not equal to 0
Range is y not equal to 2

For the inverse function,
Domain is x not equal to 2
Range is y not equal to 0
RELATED QUESTIONS
If (f)x=-(x+4)^2+3, find the domain and rage of... (answered by Fombitz)

The function f is one-to-one, find its inverse and determine the domain and range of both (answered by stanbon)

Find the inverse of f(x)=2^x. What is the domain and range of f(x)=2^x and its... (answered by Fombitz)

If f(x)={{{x^3+1}}} and {{{f^-1}}} is the inverse function of f, what is... (answered by ankor@dixie-net.com)

For a one-to-one function f(x) and its inverse function f^-1(x), the domain of f(x) is... (answered by Fombitz)

3.14 Given f(x)=x-4 and g(x)=4x^2, find f+g, f-g, fg, and f/g. Determine the domain... (answered by ikleyn)

what is the domain and range of the inverse of the f(x)=... (answered by edjones)

Let f(x) = (x-8)^2 Find a domain on which f is one to one and non decreasing Answer=... (answered by Theo)

What is the domain of f(x)= x^2 - 5x + 7 and of its derivative f '(x)=2x - 5? and then... (answered by stanbon)