Answer: f⁻¹(x)=(x-7)²
Step-by-step explanation:
To find the inverse function, we want to switch the y with the x and vice versa. Then we solve for y.
[switch y with x and x with y]
[subtract both sides by 7]
[square both sides]
Now, we know that f⁻¹(x)=(x-7)².
Answer: A Single Solution
Step-by-step explanation:
Answer:
The value of x = 4
Step-by-step explanation:
In this question, we are asked to calculate the value of the angle x
Here the ray cuts the angle into half.
Since the total of the angle was 120, half of this would be 120/2 = 60
Now, it is this value of 60, that our new angle equals to
Mathematically;
3x + 48 = 60
3x = 60-48
3x = 12
x = 12/3
x = 4
Answer:
<h3>1</h3>
Step-by-step explanation:
The nth term of an exponential sequence is expressed as ar^n-1
The nth term of a linear sequence is expressed as Tn = a + (n-1)d
a is the first term
r is the common ratio
d is the common difference
n is the number of terms
Let the three consecutive terms of an exponential sequence be a/r, a and ar
second term of a linear sequence = a +d
third term of a linear sequence = a + 2d
sixth term of a linear sequence = a + 5d
Now if the three consecutive terms of an exponential sequence are the second third and sixth terms of a linear sequence, this is expressed as;
a/r = a + d ..... 1
a = a + 2d ..... 2
ar = a+ 5d .... 3
From 2: a = a + 2d
a-a= 2d
0 = 2d
d = 0/2
d = 0
Substitute d = 0 into equation 1:
From 1: a/r = a + d
a/r = a+0
a/r = a
Cross multiply
a = ar
a/a = r
1 = r
Rearrange
r = 1
<em>Hence the common ratio of the exponential sequence is 1</em>
First of all, we need all logarithms to have the same base. So, we use the formula
To change the second term as follows:
Finally, using the property
we have
So, the equation becomes
We can now use the formula
to write the equation as
Now consider both sides as exponents of 2:
This equation has no "nice" solution, so I guess the problem is as simplifies as it can be
