(f∘g)(x) is equivalent to f(g(x)). We solve this problem just as we solve f(x). But since it asks us to find out f(g(x)), in f(x), each time we encounter x, we replace it with g(x).
In the above problem, f(x)=x+3.
Therefore, f(g(x))=g(x)+3.
⇒(f∘g)(x)=2x−7+3
⇒(f∘g)(x)=2x−4
Basically, write the g(x) equation where you see the x in the f(x) equation.
f∘g(x)=(g(x))+3 Replace g(x) with the equation
f∘g(x)=(2x−7)+3
f∘g(x)=2x−7+3 we just took away the parentheses
f∘g(x)=2x−4 Because the −7+3=4
This is it
g∘f(x) would be the other way around
g∘f(x)=2(x+3)−7
now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them.
g∘f(x)=2x+6−7
Next, +6−7=−1
g∘f(x)=2x−1
Its a lts easier than you think!
Hope this helped
Answer: x = -2
Step-by-step explanation: 3x+7 = -x-1; add 1 to both sides: 3x+8=-x; subtract 3x from both sides: 8 = -4x; divide by -4 on both sides: -2 = x
Answer:
![h=\frac{1}{6}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B1%7D%7B6%7D)
Step-by-step explanation:
Given:
![A=\frac{1}{2h} (B+b)\\](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2h%7D%20%28B%2Bb%29%5C%5C)
![A=21, B=2, b=5 ,h= ?](https://tex.z-dn.net/?f=A%3D21%2C%20B%3D2%2C%20b%3D5%20%2Ch%3D%20%3F)
We have to find the value of 'h'
So, putting the given values in the equation to find the value of 'h'.
![A=\frac{1}{2h} (B+b)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2h%7D%20%28B%2Bb%29)
Implementing the given values in the given equations:
![21=\frac{1}{2h}(2+5)\\\\ 21=\frac{1}{2h} (7)\\\\\frac{1}{2h}=\frac{21}{7}\\\\ \frac{1}{2h}=3 \\\\h=\frac{1}{6}](https://tex.z-dn.net/?f=21%3D%5Cfrac%7B1%7D%7B2h%7D%282%2B5%29%5C%5C%5C%5C%2021%3D%5Cfrac%7B1%7D%7B2h%7D%20%287%29%5C%5C%5C%5C%5Cfrac%7B1%7D%7B2h%7D%3D%5Cfrac%7B21%7D%7B7%7D%5C%5C%5C%5C%20%20%5Cfrac%7B1%7D%7B2h%7D%3D3%20%5C%5C%5C%5Ch%3D%5Cfrac%7B1%7D%7B6%7D)
So, the value of 'h' is
![h=\frac{1}{6}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B1%7D%7B6%7D)
Let w be the width and l the length of the rectangle.
Then:
![\frac{l}{w}= \frac{1+\sqrt5}{2} \text{ and }lw=104](https://tex.z-dn.net/?f=%20%5Cfrac%7Bl%7D%7Bw%7D%3D%20%5Cfrac%7B1%2B%5Csqrt5%7D%7B2%7D%20%20%5Ctext%7B%20and%20%7Dlw%3D104)
Solving the above system we get:
![l= \frac{1+\sqrt5}{2}w\\= \frac{1+\sqrt5}{2}\frac{104}{l}](https://tex.z-dn.net/?f=%20l%3D%20%5Cfrac%7B1%2B%5Csqrt5%7D%7B2%7Dw%5C%5C%3D%20%5Cfrac%7B1%2B%5Csqrt5%7D%7B2%7D%5Cfrac%7B104%7D%7Bl%7D)
Therefore:
![l^2=\frac{1+\sqrt5}{2}104](https://tex.z-dn.net/?f=l%5E2%3D%5Cfrac%7B1%2B%5Csqrt5%7D%7B2%7D104)
then
![l=13](https://tex.z-dn.net/?f=l%3D13%20)
,which is the length,
And then the width