How do you solve fog and GOF?

(fog)(x) = f(g(x)) = f(x2) = x2-2. (gof)(x) = g(f(x)) = g(x-2) = (x-2)2 = x2-4x+4. Note that fog = gof. For composition, order matters.

Accordingly, how do you do fog and GOF?

Substitute g(x) for x in f(x) to get (fOg)(x): f((g(x)) = 2 (g(x) = 2(x+3) = 2x+6. To get (gof)(x), substitute f(x) for x in g(x): (gof)(x) = (2x) + 3 = 2x+3.

Additionally, how do you do fog in math? It is actually a composition of two functions i.e. fog(x) = f(g(x)) where f(x) is the outer function and g(x) is the inner function.

Let me illustrate it with an example.

Let f(x) = 2x-1 and g(x) = (x+5)/2. Find the function (fog)(x).
Simplify your answer.
g(x) = (x+5)/2.
= 2[(x+5)/2]-1.
= x+5-1.
= x+4.

Also know, what does fog and GOF mean?

g o f means f(x) function is in g(x) function. solution : f o g means g(x) function is in f(x) function. This means put x = 2x -3 in f(x) function.

How do you find fog 1?

Answers and Replies Yes you're right (f o g)(1) is composition of functions, so f(g(1). So if f(x) = 2x + 3 then f(g(x)) = 2*g(x) + 3. Now that you have that, it should be pretty easy to find the answer.

31 Related Question Answers Found

What is inverse of a function?

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x.

How do you find the difference quotient?

Steps to Solve

Plug x + h into the function f and simplify to find f(x + h).
Now that you have f(x + h), find f(x + h) - f(x) by plugging in f(x + h) and f(x) and simplifying.
Plug your result from step 2 in for the numerator in the difference quotient and simplify.

How do you find the domain?

For this type of function, the domain is all real numbers. A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign.

How do you find the domain of a composite function?

How To: Given a function composition f(g(x)) f ( g ( x ) ) , determine its domain.

Find the domain of g .
Find the domain of f .
Find those inputs, x , in the domain of g for which g(x) is in the domain of f . That is, exclude those inputs, x , from the domain of g for which g(x) is not in the domain of f .

What is fog made of?

Like clouds, fog is made up of condensed water droplets which are the result of the air being cooled to the point (actually, the dewpoint) where it can no longer hold all of the water vapor it contains. For clouds, that cooling is almost always the result of rising of air, which cools from expansion.

What does G Circle F mean?

The symbol for composition is a small circle: (g º f)(x) It is not a filled in dot: (g · f)(x), as that means multiply.

What is the range of fog?

The international definition of fog is a visibility of less than 1 kilometre (3,300 ft); mist is a visibility of between 1 kilometre (0.62 mi) and 2 kilometres (1.2 mi) and haze from 2 kilometres (1.2 mi) to 5 kilometres (3.1 mi).

How do you identify the domain and range of a function?

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

How do I find the average rate of change?

When you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. f(x) = x² and f(x + h) = (x + h)² Therefore, the slope of the secant line between any two points on this function is 2x + h.

How find the range of a function?

Overall, the steps for algebraically finding the range of a function are:

Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x).
If you can't seem to solve for x, then try graphing the function to find the range.

What is a composite function example?

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function. For example, f(g(x)) is the composite function that is formed when g(x) is substituted for x in f(x). In the composition (f ο g)(x), the domain of f becomes g(x).

What is the derivative of f 3x?

The slope of a line like 2x is 2, or 3x is 3 etc.

Derivative Rules.

Common Functions	Function	Derivative
Reciprocal Rule	1/f	−f'/f²
Chain Rule (as "Composition of Functions")	f º g	(f' º g) × g'
Chain Rule (using ' )	f(g(x))	f'(g(x))g'(x)
Chain Rule (using d dx )	dy dx = dy du du dx

Is fog the same as GOF?

Then f and g are both one-to-one and additive, and you can check that fog(r+s√2)=s+2r√2 but gof(r+s√2)=2s+r√2. So in this case fog is not equal to gof. If you want functions defined on the whole of R, the situation is the same as in the previous paragraph.

What does the circle mean in algebra?

The circle ∘ is the symbol for composition of functions. In General, if you have two functions g:X→Y and f:Y→Z, then f∘g is a function from X to Z.

How do you solve inverse functions?

Finding the Inverse of a Function

First, replace f(x) with y .
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y .
Replace y with f−1(x) f − 1 ( x ) .
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

How do functions work?

A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.

What is chain rule in calculus?

The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².