# Thread: Solving for an inverse function

1. ## Solving for an inverse function

Help me solve these questions please and thank you.

1. Given f(x) = x2 + 3x -3 and g(x) = f -1(x) , find the value(s) of g(1).

2. given the function f(x) = 5/ 5x-16
a) Determine the inverse function
b) Explain how to find the domain and range of the function and its inverse.

3. a) Explain how you can use algebraic reasoning, rather than a vertical line test , to decide if a relation is a function?

b) How can you determine if the inverse of a function is a function by looking at the original graph of the function?

2. ## Re: Solving for an inverse function

Originally Posted by sabiha1995
Help me solve these questions please and thank you.

1. Given f(x) = x2 + 3x -3 and g(x) = f -1(x) , find the value(s) of g(1).

2. given the function f(x) = 5/ 5x-16
a) Determine the inverse function
b) Explain how to find the domain and range of the function and its inverse.

3. a) Explain how you can use algebraic reasoning, rather than a vertical line test , to decide if a relation is a function?

b) How can you determine if the inverse of a function is a function by looking at the original graph of the function?
1. hint .. $\displaystyle f(x) = 1 \implies g(1) = x$

2. a) $\displaystyle x = \frac{5}{5y-16}$ ... solve for $\displaystyle y = f^{-1}(x)$

b) since an inverse swaps the x and y values of a function, what would that do to the domain and range?

3. a) f(x) be a unique value for every value of x in the domain

b) heard of the horizontal line test?

3. ## Re: Solving for an inverse function

Originally Posted by skeeter
1. hint .. $\displaystyle f(x) = 1 \implies g(1) = x$

2. a) $\displaystyle x = \frac{5}{5y-16}$ ... solve for $\displaystyle y = f^{-1}(x)$

b) since an inverse swaps the x and y values of a function, what would that do to the domain and range?

3. a) f(x) be a unique value for every value of x in the domain

b) heard of the horizontal line test?
I wonder how is g defined in this case

4. ## Re: Solving for an inverse function

Originally Posted by psolaki
I wonder how is g defined in this case
apparently, not as a function ...

... find the value(s) of g(1).

5. ## Re: Solving for an inverse function

Originally Posted by skeeter
apparently, not as a function ...
if as a relation then how dowe define the composition of gof??

6. ## Re: Solving for an inverse function

Originally Posted by psolaki
if as a relation then how dowe define the composition of gof??
If f is a function and g is its inverse function, then $\displaystyle f \circ g = g \circ f = x$

I don't believe function composition can be applied to relations in general. I'm not an algebraist, so I would need to rely on someone with more knowledge to answer this query.