Answer: Second option from the top
Step-by-step explanation:
First, we will simplify the given inequalities.
2x + 7 ≥ 1
2x ≥ -6
x ≥ -3
-
8 -
≤ 5
-
≤ 5
-
≤ -3
x ≥ 9
Now, we will graph them. <em>See attached</em>.
The intersection would be at the point (2, 2).
This is because, graphically, the plots of f(x) and its inverse are reflections of one another across the line y = x, and (2, 2) lies on this line.
Put another way, we have f(2) = 2 = f⁻¹(2), so both f(x) and f⁻¹(x) intersect when x = 2.
Put yet another (longer) way, we can find the equation for f(x): it's a line that passes through (0, 6) and (3, 0), so it has slope -6/3 = -2. Then using the point-slope formula,
y - 6 = -2 (x - 0) ⇒ y = f(x) = -2x + 6
By definition of function inverse, we have
f(f⁻¹(x)) = x
so that with the given definition of f(x), we get
f(f⁻¹(x)) = -2 f⁻¹(x) + 6 = x
-2 f⁻¹(x) = x - 6
f⁻¹(x) = -x/2 + 3
Then we solve for x such that f(x) = f⁻¹(x). We would find x = 2 as before.
Answer:
![\huge \boxed{{y=2x+5}}](https://tex.z-dn.net/?f=%5Chuge%20%5Cboxed%7B%7By%3D2x%2B5%7D%7D)
Step-by-step explanation:
y = mx + b (slope-intercept form of a line)
m is slope
b is y-intercept
The y-intercept of the line is (0, 5) or 5.
y = mx + 5
The slope of the line can be found through rise over run.
(1, 7) and (2, 9) are two points on the line.
m = (y2-y1)/(x2-x1)
m = (9 - 7)/(2 - 1)
m = 2/1 = 2
The slope of the line is 2.
y = 2x + 5