Thread: 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?

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 ..

2. a) ... solve for

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?

Originally Posted by skeeter

1. hint ..

2. a) ... solve for

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

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).

Originally Posted by skeeter

apparently, not as a function ...

if as a relation then how dowe define the composition of gof??

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

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.