If f(x)=1/(3x-2), then f^-1(x)=?
Simplify y^(2/7) * y^(14/2)
And one more
f(x) = 1/(3x-2)
To find f^-1(x), you switch x and f(x). For ease of typing, lets use y instead of f(x). Then, y=1/(3x-2). Switching, you get x=1/(3y-2). Then you solve for y. Multiply both sides by (3y-2), and you have 3xy-2x=1. Then adding 2x to each side is 3xy=2x+1. Finally, divide each side by 3x, and you have y=2/3*1/3x=f^-1(x)
When you’re multiplying two things with the same base, you simply add the powers. Thus,
Then you need a common denominator to add the fractions. The least common multiple of 7 and 2 is 14 (which is 7*2), you you can then get
When simplifying expressions like this, you need to multiply the two exponents together. Thus, (2/7)*(14/2)=(2*14/7*2). Note the 2’s cancel, leaving 14/7, which simplifies to 2. Then, you have
I hope that helped! The answers should be right. Although I didn’t double check my work… The methods are definitely correct, though!