Can somebody help me please
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
In order to find the inverse of a function, we need to follow a couple of steps.
- Step 1: Write the function as
- Step 2: Swap all x and y values
- Step 3: Solve for y
- Step 4: Replace y with
We can follow these steps to find the inverse of this function.
Step 1: We can just replace the f(x) with y, making our function .
Step 2: We can swap where the x and y values are, making our equation
Step 3: We can now solve for y.
We now have the function as .
Step 4: We can now replace the y with .
Therefore the inverse of is
.
Hope this helped!
Answer:
a) 3
b) 9
c) 81
d) x
Step-by-step explanation:
We know the properties of log function as:
1) log(AB) = log(A) + log(B)
2)
3) log(aᵇ) = b × log(a)
also,
4)
Given:
a. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(3) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = 1 × log(3)
taking anti-log both sides
y = 3
b. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(9) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(9)
taking anti-log both sides
y = 9
c. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(81) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(81)
taking anti-log both sides
y = 81
d. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(x) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(x)
taking anti-log both sides
y = x