I don’t know what is your problem is
Hi!
We can see here that this is a composition question.
And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).
To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.
![f(x)=\frac{e^7^x+\sqrt{3}}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Be%5E7%5Ex%2B%5Csqrt%7B3%7D%7D%7B2%7D)
![y=\frac{e^7^x+\sqrt{3}}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Be%5E7%5Ex%2B%5Csqrt%7B3%7D%7D%7B2%7D)
![x=\frac{e^7^y+\sqrt{3}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Be%5E7%5Ey%2B%5Csqrt%7B3%7D%7D%7B2%7D)
![2x=e^7^y+\sqrt{3}](https://tex.z-dn.net/?f=2x%3De%5E7%5Ey%2B%5Csqrt%7B3%7D)
![e^7^y=2x-\sqrt{3}](https://tex.z-dn.net/?f=e%5E7%5Ey%3D2x-%5Csqrt%7B3%7D)
![7y=ln(2x-\sqrt{3})](https://tex.z-dn.net/?f=7y%3Dln%282x-%5Csqrt%7B3%7D%29)
![y=\frac{ln(2x-\sqrt{3})}{7}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bln%282x-%5Csqrt%7B3%7D%29%7D%7B7%7D)
Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.
![g(f(x))](https://tex.z-dn.net/?f=g%28f%28x%29%29)
![g(\frac{e^7^x+\sqrt{3}}{2})](https://tex.z-dn.net/?f=g%28%5Cfrac%7Be%5E7%5Ex%2B%5Csqrt%7B3%7D%7D%7B2%7D%29)
![\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bln%282%28%5Cfrac%7Be%5E7%5Ex%2B%5Csqrt%7B3%7D%7D%7B2%7D%29-%5Csqrt%7B3%7D%7D%7B7%7D)
2s cancel.
![\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}](https://tex.z-dn.net/?f=%5Cfrac%7Bln%28e%5E7%5Ex%2B%5Csqrt%7B3%7D%29-%5Csqrt%7B3%7D%7D%7B7%7D)
The natural log and e cancel.
![\frac{7x+\sqrt{3}-\sqrt{3}}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%2B%5Csqrt%7B3%7D-%5Csqrt%7B3%7D%7D%7B7%7D)
s cancel.
![\frac{7x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%7D%7B7%7D)
7s cancel.
![x](https://tex.z-dn.net/?f=x)
Hope this helps!
It’s c because I got it right on the test
Answer:
-23.21
Step-by-step explanation:
Edge 2021