Lesson: Function Notation

Question link: https://gmatclub.com/forum/if-f-x-3x-x-and-g-x-x-2-what-is-f-g-209750.html

The notation f(g(4)) represents the value of the function (f) when we input the value of g(4)

So, in this example, g(4) = 4² = 16

So, f(g(4)) = f(16) [now we must evaluate f(16)]

f(16) = 3(16) − √16
= 48 - 4
= 44

So, to recap, f(g(4)) = f(16) = 44

Does that help?

Cheers,
Brent

I'm happy to help.
Here's my full solution: https://gmatclub.com/forum/for-which-of-the-following-functions-is-f-a-b...

Cheers,
Brent

Question link: https://gmatclub.com/forum/the-functions-f-and-g-are-defined-as-f-x-2x-3...

If f(x) = 2x – 3, then f(7) = 2(7) – 3
And f(19) = 2(19) – 3
And f(5.5) = 2(5.5) – 3
....and f(y) = 2y – 3

The main idea here is that we can input anything into the function named "f"
The function, f, tells us to take the inputted value, double it and then subtract 3.
So, we can also say that....
f(14) = 2(14) – 3
And f(k²) = 2(k²) – 3
And f(4q + 1) = 2(4q + 1) – 3

Does that help?

Cheers,
Brent

I believe you're referring to this super difficult question: https://gmatclub.com/forum/if-f-x-is-a-function-what-is-the-value-of-f-2...

As you suggested, in MOST cases, the function looks something like f(x) = x²
So, f(3) = 3² = 9
And f(-11) = (-11)² = 121
And even f(x + 5) = (x + 5)² = x² + 10x + 25

That said, the function f(4x) = 8x² − 1 isn't much different from the function g(k) = 8k² − 1

To find the value of g(3), we replace k with 3 to get: g(3) = 8(3²) − 1 = 71
However, since f(4x) requires us to multiply the x-value by 4, we must do a little work before we can find the value of f(3)

To find the value of f(3), we need to first find the value of x such that 4x = 3.
Since x = 0.75 is the solution to the equation 4x = 3, we can know that, in order to evaluate f(3), we need x to be 0.75
In other words, f(3) = f[(4)(0.75)] = 8(0.75²) − 1 = 4.5 - 1 = 3.5

Does that help?