Functions

It is certain that you will find questions based on functions in GRE. Even a single question can make a huge difference in a Standardized test like GRE. So, it is important to tackle this topic before the D-day and make it your friend.

What is Function?

If you are confused with the concepts of functions, then let’s break it and make it understandable. Imagine functions as a recipe. What does a recipe do? It specifies some steps to cook the desired dish, similar functions also specify certain operations that after performing you can reach some specified output. Just because it has a strange notation, it should not intimidate you because functions are nothing but simple substitution.

Let’s take an example:

If, for all values of x, \(f(x) = 7x + 3\) hen find \(f(3)\)

Solution: \(f(x) = 7x + 3\)

\(f(3) = 7(3) + 3 = 24\)

Here, it is important to note that f(x) does not mean that ‘f’ is multiplied with ‘x’. Here the term inside the parenthesis represents the input value of the function. In other words, as described through the recipe method, this formula explained by f(x) tells you to get the value asked you must multiply the function f with the value present inside the parenthesis. Now with this definition it will become easier for you to understand the example explained above.

Now, in the previous example, the formula for the function was given along with its input and you had to get the output based on the input value.

But GRE won’t always ask the straight-forward questions. Sometimes they would ask you to find the input value based on the output result given. Sometimes, you will have the function formula along with the output and through that output you have to find the input value.

For example: For all positive value of x, \(f(x) = (x -2)^{2} + 5, \; if, \; f(a) = 60\), then find the value of ‘a’.

It should be noted that in the above question, the function values apply only to positive values of ‘x’. For solving this question, similar substitution process is to be followed.

Now, let’s solve this question.

\(Step \; 1 -\) Put ‘a’ into the function. So,  \(f(a) = (a – 2)^{2} – 4\)
\(Step \; 2 -\) Now, put the equation equal to 60; \((a – 2)^{2} – 4 = 60\)
\(Step \; 3 -\) Now, solve for a, \((a – 2)^{2} = 64\)
\((a – 2) = 8\)
\(a = 10\)

So, solve functions and with some extra efforts you can conquer it.

Also Read

Graphs of Functions

Algebra Applications

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