Answer: 
Step-by-step explanation:
By definition, a relation is a function if and only if each input value has one and only one output value.
For this exercise it is important to remember that thw "Input values" are the values of the variable "x"and the "Output values" are the values of the variable"y".
In this case you have the following function provided in the exercise:

Then, to solve this exercise, you need to follow these steps:
Step 1. You have to substitute
into the function given.
Step 2. Finally, you must evaluate in order to find the corresponding output value (or the value of the variable "y")
You get that this is:

Answer:
Step-by-step explanation:
A quadratic equation can be factorised if and only if there are rational roots.
For any quadratic equation the discriminant decides about the nature of roots.
Thus only if the discriminant is a perfect square we can have rational roots and in this case only factorization is possible.
In the given equation

Since 1 is a perfect square we can factor and solve

Answer:
b) f(x) = x + 6
Step-by-step explanation:
The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.
there are many combinations for it, but we can settle for say
![\bf \begin{cases} f(x)=x+2\\[1em] g(x)=\cfrac{9}{x^2}\\[-0.5em] \hrulefill\\ (f\circ g)(x)\implies f(~~g(x)~~) \end{cases}\qquad \qquad f(~~g(x)~~)=[g(x)]+2 \\\\\\ f(~~g(x)~~)=\left[ \cfrac{9}{x^2} \right]+2\implies f(~~g(x)~~)=\cfrac{9}{x^2}+2](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20f%28x%29%3Dx%2B2%5C%5C%5B1em%5D%20g%28x%29%3D%5Ccfrac%7B9%7D%7Bx%5E2%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20%28f%5Ccirc%20g%29%28x%29%5Cimplies%20f%28~~g%28x%29~~%29%20%5Cend%7Bcases%7D%5Cqquad%20%5Cqquad%20f%28~~g%28x%29~~%29%3D%5Bg%28x%29%5D%2B2%20%5C%5C%5C%5C%5C%5C%20f%28~~g%28x%29~~%29%3D%5Cleft%5B%20%5Ccfrac%7B9%7D%7Bx%5E2%7D%20%5Cright%5D%2B2%5Cimplies%20f%28~~g%28x%29~~%29%3D%5Ccfrac%7B9%7D%7Bx%5E2%7D%2B2)