# Find “gof” and “fog”where:

\[f(x) = x - 2,\,g(x) = {x^2} + 3x + 1\]?

Answer

Verified

279.6k+ views

**Hint:**Here the given question is to find the value of “gof” and “fog” for the given value of the functions, here we know that to obtain the “fog” or “gof”, we need to understand the meaning of “fog” and “gof”, here “fog” means that g(x) function is inside the f(x) function and value of g(x) will be replaced on place of “x” in the “f(x)” function, and respectively for the “gof” also.

**Complete step-by-step solution:**

Here the given question is to find the value for the given functions, here the property of the “gof” and “fog” is to be used, we already know the meaning of both the functions, now on solving for the values of the functions we get:

First of all dealing with “gof” we get:

\[\Rightarrow gof = {(x - 2)^2} + 3(x - 2) + 1 \\

\Rightarrow gof = {x^2} - 4x + 4 + 3x - 6 + 1 \\

\Rightarrow gof = {x^2} - x - 1 \]

Now solving for “fog” we get:

\[ \Rightarrow fog = ({x^2} + 3x + 1) - 2 \\

\Rightarrow fog = {x^2} + 3x + 1 - 2 = {x^2} + 3x - 1 \]

Here we get the values for the functions.

**Note:**Here the given question is to solve for the function “fog and gof”, here we can not find the value without getting the meaning of the terms, and as we know that these functions required to solve after putting the value of one function into other and then solve further and get the solution.

Recently Updated Pages

Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Scroll valve is present in a Respiratory system of class 11 biology CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

is known as the Land of the Rising Sun A Japan B Norway class 8 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE