Fog and Gof Math Problems

Introduction to fog and gof math problems:
Basically fog and gof math problems are nothing but we have to convert the one function into other function. If the given function is in the form of f(x) mean we have to convert this into f (g (x)) form. If the given function is in the g (x) form then we have to change this into g (f (x)) form.  Let us see some example for these types of problems.


Example for fog and gof math problems


Example 1:

Find the fog and gof for the given math problems. Where f (x) = x and g (x) = 3x + 4

Solution:

First we have to find fog for the given problem.  For that first we have to find the g(x).

Where g (x) = 3x + 4

fog = f (g (x)) = f (3x + 4) = 3x + 4

Likewise we have to find gof for the given math problem.

gof mean first we have to find f(x)

Where f (x) = x

Then gof = g (f (x)) = g (x) = 3x +4

From the above we understand we have to write the output of the one function value into the other function form.

Understanding Graphing Quadratic Functions in Standard Form is always challenging for me but thanks to all math help websites to help me out.

Example 2:


Find the fog and gof for the given math problems. Where f(x) = 2x + 5 and g(x) = 5x

Solution:

First we have to find fog for the given problem.  For that first we have to find the g(x).

Where g (x) = 5x

fog = f (g (x)) = f (5x) = 2(5x) + 5

= 10x + 5

Likewise

gof mean first we have to find f(x)

Where f (x) = 2x + 5

Then gof = g (f (x)) = g (2x + 5) = 5(2x + 5)

= 10x + 25

If suppose we are having the square or cubic function mean we have to find the square or cubic roots. After that we have to expand the function. From the above there is no square or cubic value. So we just find the function values.