1.) Consider the graphs x+5y=17 and x+7=y^2
where
a=7
b=2
c=57
f(x) = ?
g(x) = ?
I have solved for a,b, and c but I can't figure out f(x) and g(x)
For f(x) I thought it was (17-x)/5 but it's not the correct answer.
For g(x) I thought it was the sqrt(x+7) but it's also not the correct answer.
What am I doing wrong?
Nevermind, solved it!
To find the functions f(x) and g(x) given the equations x+5y=17 and x+7=y^2, we need to isolate the variables x and y in each equation.
Let's start with f(x):
1.) x + 5y = 17
We can solve this equation for y by isolating it:
2.) 5y = 17 - x
3.) y = (17 - x)/5
So, you were correct in getting f(x) as (17 - x)/5.
Now, let's move on to g(x):
1.) x + 7 = y^2
We want to solve this equation for y, so let's isolate y:
2.) y^2 = x + 7
Here's where your mistake lies. To find g(x), we need to take the square root of both sides of the equation, giving us:
3.) y = ±√(x + 7)
So, g(x) should be g(x) = ±√(x + 7). The ± sign indicates both the positive and negative square root solutions.
Therefore, the correct expressions for f(x) and g(x) are:
f(x) = (17 - x)/5
g(x) = ±√(x + 7)