Lesson: Function Notation

There are no rules regarding how to name/denote functions, however, I chose to name the function "C" since we'll use it to determine the Cost of the trip.

Likewise, if I create a function to determine the Height of a ball t seconds after it is tossed, I might name the function "H" to indicate that the function outputs the Height of the ball, as in H(t) = 20 - 4.9t²

The input value in my example is x represents the number of miles driven.
I could also have defined the cost function as C(m) = 1.50m + 2.50, where m represents the number of miles driven.

Your function,f(c) = 1.50m + 2.50, has a few issues.
The biggest problem is that is asks us to enter a c-value, but the expression (formula) does not contain any c's. To fix it, we might write f(c) = 1.50c + 2.50

Of course, it's important to also note that c represents the number of miles driven, and NOT the cost of the trip.

Question link: https://gre.myprepclub.com/forum/assume-the-function-f-x-is-defined-as-f...

If ANY part of the expression is undefined, then the entire expression is undefined.
If EVERY part of the expression is defined, then the entire expression is defined.

For example, 2 and 5 are both defined.
So, the sum, 2 + 5, is defined.
We know this, because 2 + 5 = 7, and 7 is defined.

Here's a different example:
2 is defined, but 1/0 is undefined.
So, the sum, 2 + 1/0, is undefined.
We know this, because the sum, 2 + 1/0, does not have a definite value.

Does that help?

Cheers,
Brent

Here's the video on factoring quadratics: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

We want to factor n² - 24n - 145

We're looking for two values that have a product of 145 AND a sum of -24

So, start looking for pairs of number that have a product of 145
For each pair of values, we'll ask "Can we get a sum of -24 with this pair?"

1 and 145
"Can we get a sum of -24 with this pair? No.

5 and 29
"Can we get a sum of -24 with this pair?
YES!
5 + (-29) = -24

So, n² - 24n - 145 = (x + 5)(x - 29)

Cheers,
Brent

Question link: https://gre.myprepclub.com/forum/challenge-if-f-3x-2-9x-12x-1-then-f-k-1...

We can't assume that k - 1 = 3x + 2. Here's why:

We're told that f(3x + 2) = 9x² + 12x - 1
IF it were the case that f(k - 1) = 9k² + 12k - 1, then we could assume that k - 1 = 3x + 2 [since both inputs yield the same output]

However, we don't know what the output for f(k - 1) is.

Does that help?

Cheers,
Brent

Hi Sri,

Great observation!
It turns out that we don't even need to use the given information that f(3) = 1/2

If f(t) = kt, then f(1) = k(1) = k, which means the two quantities are equal.
Great work!

Question link: https://gre.myprepclub.com/forum/if-f-2x-1-4x-4x-8-then-f-10361.html

Notice that, if x = 3, then 2x-1 = 5
In other words, when x = 3, (2x - 1) and 5 have the same value.
In other words, when x = 3, f(2x - 1) = f(5)

So, f(5) = f[2(3) - 1] = 4(3²) - 4(3) - 8

Does that help?

By the way, I added one more solution to the question here: https://gre.myprepclub.com/forum/if-f-2x-1-4x-4x-8-then-f-10361.html#p51690

We don't have any topic-wise tests, but you can create topic-wise tests by using GRE Prep Club's filters.
For example, this graphic https://imgur.com/w8uo3gc shows you how to define the topic, difficulty level and source to create a list of Quantitative Comparison questions that test only Algebra.