Answer:
x+21
Step-by-step explanation:
g(x) = x - 12 and h(x) = 2x + 9,
h(x) – g(x) = 2x+9 - (x-12)
Distribute the minus sign
= 2x+9-x+12
Combine like terms
= x +21
First, find the slope using the equation m = (y2 - y1)/(x2 - x1) and then once you have it, put the slope into the equation for a line y = mx + b. So now, all that’s left is finding b so use one of the coordinate given to you and plug them in for x and y and solve for b. Once you find b, you just plug it into the equation with m and then you have your equation.
Answer:
At 53 mph, he traveled for 1.5 hours
At 58 mph, he traveled for 2 hours
Step-by-step explanation:
Mathematically;
distance = speed * time
let the time for the first part of the trip be x hours and the second part be y hours
Total hours is 3.5
So therefore;
x + y = 3.5 ••••••••(i)
Now let’s work with the rate
53 mph for x hours = 53 * x = 53x miles
58 mph for y hours = 58 * y = 58y miles
Adding both;
53x + 58y = 195.5 miles ••••••••(ii)
We have two equations to solve simultaneously
From i, x = 3.5 - y
insert into ii
53(3.5-y) + 58y = 195.5
185.5 - 53y + 58y = 195.5
5y = 195.5-185.5
5y = 10
y = 10/5
y = 2 hours
x = 3.5 - y
x = 3.5 - 2
x = 1.5 hours
Answer:
![f^{-1}(x) = \sqrt[3]{x+5}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%2B5%7D)
Step-by-step explanation:
A function 
is the inverse of f if whenever y =f(x) and 
To find the inverse of f(x) = 
- 5, we use the following steps:
- Step 1 : Put y for f(x) and solve for x
y = - 5
<=> = y + 5
<=> x = ![\sqrt[3]{y+ 5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7By%2B%205%7D)
- Step 2: Put
for x, we have:
![f^{-1}(y) =\sqrt[3]{y+5}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28y%29%20%3D%5Csqrt%5B3%5D%7By%2B5%7D)
- Step 3: Interchange y =x, we have
Let Calculate 3 points on f(x)
x = 0 => y = -5
x = 1 => y = -4
x = 2 => y = 3
Let Calculate 3 points on (x)
x = -5 => y = 0
x = -4 => y = 1
x = 3 => y = 2
Yes, the inverse is correct because:
- the domain of the inverse function is the range of the original function
- the range of the inverse function is the domain of the original function
