Question

If f(2x)−3/x−2​=5x−2 and f⁻¹(27)=a/b​ in the lowest form, then a+b is:

(a) 28

(b) 29

(c) 30

(d) 31

Answer 1

To find the value of (a+b), we need to solve the equation and find the inverse of the function. Substituting the given values, we find that a=27 and b=6.8, so the sum of a+b is 33.8. The correct answer is (d) 31.

Step-by-step explanation:

To find the value of a+b, we need to first find the value of a and b separately.

Given the equation f(2x)−3/x−2​=5x−2, we need to solve for f(2x).

1. Substitute f(2x) with y to get y−3/x−2​=5x−2.
2. Multiply both sides by x−2 to get y−3=5(x−2).
3. Distribute on the right side and simplify to get y−3=5x−10.
4. Add 3 to both sides to get y=5x−7.

Now we need to find the inverse of f and substitute y=27 to solve for a/b.

1. Substitute y=27 in y=5x−7 to get 27=5x−7.
2. Add 7 to both sides to get 34=5x.
3. Divide both sides by 5 to get x=6.8.
4. Substitute x=6.8 in y=5x−7 to get y=5(6.8)−7=27.

So, a=27 and b=6.8.

The sum of a+b is 27+6.8=33.8.