Composition of Functions
f o g(x)=f(g(x)) --> I know that this is eqivalent to f(g(x))
Given f(x) = 2x+1, and g(X) = 3x+1 find:f o g(x)=f(g(x))
This is what I did, but I don't think Ive solved it correctly
f(g(x)) = f(x-3)
f(x-3) = 1(x-3)-3x+2
=x-3-3x+2
f(g(x)) = -2x-1
The perimeter P of a square and the area A of a square r functions of its side length S. write area as function of Perimeter. ?
Also write out the square's area as function of length of its diagonal.
f(g) = 2g+1 = 2(3x+1)+1 = 6x+3
dunno where you got x-3
P = 4s
A = s^2 = (P/4)^2 = P^2/16
d = sā2
A = s^2 = (d/ā2)^2 = d^2/2
To find f o g(x), you need to substitute the function g(x) into the function f(x). Let's begin by finding g(x) using the given function:
g(x) = 3x + 1
Now, substitute g(x) into f(x):
f(g(x)) = f(3x + 1)
Next, substitute the value of g(x) into f(x) and simplify:
f(g(x)) = 2(3x + 1) + 1
= 6x + 2 + 1
= 6x + 3
Therefore, f o g(x) = 6x + 3.
Moving on to the next question:
To write the area of a square as a function of its perimeter (P), we need to determine the relationship between the area and the perimeter.
The perimeter (P) of a square is given by the equation P = 4S, where S represents the side length of the square. To find the area, we can use the formula A = S^2.
Since we already have the expression for the perimeter (P), we can substitute it into the area formula:
A = (P/4)^2
= P^2/16
Therefore, the area (A) of a square can be expressed as A = P^2/16.
Now, let's consider finding the square's area as a function of the length of its diagonal.
Given the length of the diagonal (D), we can use the Pythagorean theorem to establish the relationship between the diagonal and the side length of the square.
By the Pythagorean theorem, we have D^2 = S^2 + S^2 (since the square has four right angles).
This simplifies to D^2 = 2S^2.
To find the area (A) of the square, we multiply the side length (S) by itself:
A = S^2
Now, substitute the relationship from the Pythagorean theorem:
A = (D^2)/2
Therefore, the area (A) of a square can be expressed as A = (D^2)/2, where D represents the length of the diagonal.