Answer:
3rd option (top right)
Step-by-step explanation:
3rd option represents a linear equation
y = -2x-1
Answered by GAUTHMATH
<u>Part 1</u>
<u />![(f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1](https://tex.z-dn.net/?f=%28f%5Ccirc%20g%29%28x%29%3Df%28%5Csqrt%7Bx%7D%29%3D4%5Csqrt%7Bx%7D%2B1)
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is ![\boxed{[0, \infty)}](https://tex.z-dn.net/?f=%5Cboxed%7B%5B0%2C%20%5Cinfty%29%7D)
<u>Part 2</u>
<u />![(g \circ f)(x)=g(4x+1)=\sqrt{4x+1}](https://tex.z-dn.net/?f=%28g%20%5Ccirc%20f%29%28x%29%3Dg%284x%2B1%29%3D%5Csqrt%7B4x%2B1%7D)
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,
![4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}](https://tex.z-dn.net/?f=4x%2B1%20%5Cgeq%200%5C%5C%5C%5C4x%20%5Cgeq%20-1%5C%5C%5C%5Cx%20%5Cgeq%20-%5Cfrac%7B1%7D%7B4%7D)
Thus, the domain in interval notation is ![\boxed{\left[-\frac{1}{4}, \infty)}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cleft%5B-%5Cfrac%7B1%7D%7B4%7D%2C%20%5Cinfty%29%7D)
Answer:
y=6x+5
Step-by-step explanation: