Find f(x), if f(2b-1)=6b+2
let 2b - 1= x
2b = x+1
b = (x+1)/2
then for
f(2b-1) = 6b = 2
f(x) = 6(x+1)/2 + 2
=3(x+1) + 2
= 3x + 5
f(x) = 3x + 5
check by replacing x with 2b-1
f(2b-1) = 3(2b-1) +5 = 6b -3+5
= 6b + 2 , as given
Well, if we substitute 2b-1 into our function f(x) and solve for f(x), we get f(2b-1) = 6b + 2.
But here's the thing, we want to find f(x), not f(2b-1). So let's turn on our laughter lenses and see what we can do to solve this.
If we want f(x), we need to find a way to express x in terms of b. Any ideas on how to accomplish that? Let's get creative!
How about we start with x = 2b - 1? That way, we can substitute x in our function f(x) and make it a little more user-friendly. Ready? Let's proceed with caution.
Substituting x = 2b - 1 into f(x), we get f(x) = 6(2b - 1) + 2.
Now, all we need to do is simplify this expression. 6 times 2b gives us 12b, and 6 times -1 gives us -6. Adding 2 to that lovely mess, we end up with f(x) = 12b - 6 + 2.
Simplifying further, we get f(x) = 12b - 4. Ta-da!
So, the magical function that we've uncovered is f(x) = 12b - 4. Now, it's time to run off and impress your friends with your newfound knowledge. Enjoy!
To find f(x), we need to substitute the given value into the function. In this case, the given value is 2b-1, so we can replace x with 2b-1. Thus,
f(2b-1) = 6(2b-1) + 2.
Now we simplify the expression:
f(2b-1) = 12b - 6 + 2.
Combining like terms, we get:
f(2b-1) = 12b - 4.
Therefore, f(x) = 12x - 4.
To find f(x), we need to solve the equation f(2b - 1) = 6b + 2 and express x in terms of b.
Given that f(2b - 1) = 6b + 2, let's substitute 2b - 1 for x:
f(x) = 6( (x + 1)/2 ) + 2
Now, we can replace x with 2b - 1:
f(2b - 1) = 6( (2b - 1 + 1)/2 ) + 2
Simplifying the equation further:
f(2b - 1) = 6(2b/2) + 2
Now, canceling out common factors:
f(2b - 1) = 6b + 2
We can see that f(2b - 1) is equal to the given expression 6b + 2. Therefore, f(x) is equal to 6x + 2.