First: f(2) is same as f(x=2) so all we have to do is to express x=2 in f(x)
f(2) = 3*2 + 2 = 8
Second
f^(-1) (3) is inverse function. first we solve f(x) for x.
let f(x) be equal to some variable m
m = (2x -7)/3
3m = 2x - 7
2x = 3m + 7
x = (3m + 7)/3
now we write:
f^-1(x) = (3x + 7)/3
x=3
f^-1(3) = 16/3
Third
2y + 14 = 4y - 2
we just solve for y
2y = 16
y = 8
Now we take that f(x) = y because we both write to be the functions of x
that means that First and third have same result.
Answer:
Let's talk through this a one step at a time.
*Since f(x) is concave-up with its vertex on the x-axis, we know f(x) ≥ 0.
*We also know that when we shift a function's domain by a positive number, we shift the function left and when we shift a function's domain by a negative number, we shift the function right. So f(x-5) is f(x) shifted to the right by 5.
*At this point, f(x-5) has its vertex at (5,0).
*When we negate f(x-5), the parabola becomes concave down yet the vertex remains at (5,0). Now we're at -f(x-5). At this point we have -f(x-5)≤0 with a range (-∞,0]
*If we add 2 to create g(x)=2-f(x-5), then we have a concave down parabola with its vertex shifted up by 2, at (5,2). So, g(x) is concave down with its vertex at (5,2). Hence
Answer:
0.15
Step-by-step explanation:
5400 ÷ 37000
Cancel out extra zeros
54 ÷ 370 =
Divide and get:
0.15
Hope your boredom is cured :)
Answer:
Step-by-step explanation:
Use the slope-intercept form:
m is the slope and b is the y-intercept. Looking at the graph, you can find the y-intercept. The y-intercept is the point where x equals 0:
To find the slope, take any two points from the line:
Use the slope formula for when you have two points:
The rise over run is the change in the y-axis over the change of the x-axis. Insert the appropriate values:
Simplify parentheses (two negatives makes a positive):
Simplify (two negatives make a positive):
The slope is 
and the y-intercept is 
. Insert these into the equation:
Finito.
